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Set with operations obeying given axioms
In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection
Algebraic_structure
abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field. For example, all Jordan algebras are
Structurable_algebra
Ring that is also a vector space or a module
a ring homomorphism from K into the center of A. This is thus an algebraic structure with an addition, a multiplication, and a scalar multiplication (the
Associative_algebra
Overview of and topical guide to algebraic structures
algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures
Outline of algebraic structures
Outline_of_algebraic_structures
Algebraic structure modeling logical operations
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties
Boolean_algebra_(structure)
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Algebra based on a vector space with a quadratic form
Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished
Clifford_algebra
Albert algebra gives a form of the E7 Lie algebra. The split Albert algebra is used in a construction of a 56-dimensional structurable algebra whose automorphism
Albert_algebra
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Vector space equipped with a bilinear product
algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting
Algebra_over_a_field
Algebraic structure used in analysis
In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket
Lie_algebra
Branch of functional analysis
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with
Operator_algebra
algebra Structurable algebra Supercommutative algebra Symmetric algebra Tensor algebra Universal enveloping algebra Vertex operator algebra von Neumann
List_of_algebras
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
248-dimensional exceptional simple Lie group
of Brown's 56-dimensional structurable algebra. Allison's 5-graded Lie algebra construction based on this structurable algebra recovers the original e 8
E8_(mathematics)
Mathematical structure in abstract algebra
more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of two involutive
*-algebra
Algebraic structure with a binary operation
In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with
Magma_(algebra)
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Theory of algebraic structures in general
algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures
Universal_algebra
Associative algebra together with a Lie bracket that satisfies Leibniz's law
algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure are
Poisson_algebra
Not-necessarily-associative commutative algebra satisfying (xy)(xx) = x(y(xx))
In abstract algebra, a Jordan algebra is a nonassociative algebra (with unit) over a field whose multiplication satisfies the following axioms: x y =
Jordan_algebra
Elements taken to zero by a homomorphism
the underlying algebraic structure in the domain to its image. When the algebraic structures involved have an underlying group structure, the kernel is
Kernel_(algebra)
Algebraic structure of set algebra
a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used
Σ-algebra
Study of discrete mathematical structures
function fields. Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: Boolean algebra used in logic gates
Discrete_mathematics
Particular kind of algebraic structure
mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A {\displaystyle A} over the real or complex
Banach_algebra
Algebraic structure with addition, multiplication, and division
rational numbers do. A field is thus a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Algebraic structure used in logic
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with
Heyting_algebra
Application of mathematical methods to other fields
as a collection of mathematical methods such as real analysis, linear algebra, mathematical modelling, optimisation, combinatorics, probability and statistics
Applied_mathematics
Mapping of mathematical formulas to a particular meaning
Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is
Structure (mathematical logic)
Structure_(mathematical_logic)
Universal construction in multilinear algebra
algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras. The tensor algebra also has two coalgebra structures; one simple one, which
Tensor_algebra
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Construction in algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)
Hopf_algebra
Additional mathematical object
partial list of possible structures is measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, graphs
Mathematical_structure
Group that is also a differentiable manifold with group operations that are smooth
circle. Its Lie algebra is (more or less) the Witt algebra, whose central extension the Virasoro algebra (see Virasoro algebra from Witt algebra for a derivation
Lie_group
Class of algebraic structures
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of
Variety_(universal_algebra)
Algebra over a field where binary multiplication is not necessarily associative
A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative
Non-associative_algebra
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Algebraic structure in homological algebra
homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used
Differential_graded_algebra
Branch of mathematics concerning probability
any set Ω {\displaystyle \Omega \,} (also called sample space) and a σ-algebra F {\displaystyle {\mathcal {F}}\,} on it, a measure P {\displaystyle \mathbb
Probability_theory
Algebraic structure with only one element
In algebra, the zero object of a given algebraic structure is, in the sense explained below, the simplest object of such structure. As a set it is a singleton
Zero_object_(algebra)
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
Area of mathematics
algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics
Computational_mathematics
computer algebra system (CAS) is a software product designed for manipulation of mathematical formulae. The principal objective of a computer algebra system
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding
Level structure (algebraic geometry)
Level_structure_(algebraic_geometry)
Calculus of vector-valued functions
generalize to higher dimensions, but the alternative approach of geometric algebra, which uses the exterior product, does (see § Generalizations below for
Vector_calculus
Sequence of operations for a task
beyond specific numerical solutions to introduce general procedures for algebraic reduction and balancing. This transformed mathematics into a 'mechanical'
Algorithm
Magma obeying the Latin square property
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible
Quasigroup
Equivalence relation in algebra
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector
Congruence_relation
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Study of the properties of codes and their fitness
needed] The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then
Coding_theory
Field of mathematics
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which
Numerical_linear_algebra
Branch of mathematics
firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, particularly by Euler. Instead, Cauchy formulated
Mathematical_analysis
Algebraic variety with a group structure
mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus
Algebraic_group
Setting of relativistic physics in geometric algebra
spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra provides
Spacetime_algebra
Algebraic construct of interest in theoretical physics
noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix
Quantum_group
Unix-like systems. KCalc, Linux based scientific calculator Maxima: a computer algebra system which bignum integers are directly inherited from its implementation
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
Theory of subatomic structure
called algebraic varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic illustrated on the right is an algebraic variety
String_theory
Study of abstract machines and automata
nondeterministic finite automata. In the 1960s, a body of algebraic results known as "structure theory" or "algebraic decomposition theory" emerged, which dealt with
Automata_theory
Algebraic structure
algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are
Interior_algebra
Set whose pairs have minima and maxima
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered
Lattice_(order)
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Coefficients of an algebra over a field
In mathematics, the structure constants or structure coefficients of an algebra over a field are the coefficients of the basis expansion (into linear
Structure_constants
postulate. Abstract algebra The part of algebra devoted to the study of algebraic structures in themselves. Occasionally named modern algebra in course titles
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Computer system for solving algebra problems
computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma
Magma (computer algebra system)
Magma_(computer_algebra_system)
Branch of mathematics that studies algebraic structures
algebra in Wiktionary, the free dictionary. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures
List of abstract algebra topics
List_of_abstract_algebra_topics
Group of mathematical theorems
modules, Lie algebras, and other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences
Isomorphism_theorems
supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains
Supersymmetry_algebra
Physical theory with fields invariant under the action of local "gauge" Lie groups
the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises
Gauge_theory
Concept in mathematics
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal
Universal_enveloping_algebra
Software used in mathematical applications
mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human
Mathematical_software
Result of partitioning the elements of an algebraic structure using a congruence relation
a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are also called
Quotient_(universal_algebra)
Algebraic structure
In mathematics, a J-structure is an algebraic structure over a field related to a Jordan algebra. The concept was introduced by Springer (1973) to develop
J-structure
Branch of mathematics
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins
Homological_algebra
algebra is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector algebra
Comparison of vector algebra and geometric algebra
Comparison_of_vector_algebra_and_geometric_algebra
Branch of algebra that studies commutative rings
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both
Commutative_algebra
Branch of applied mathematics
some parts of the mathematical fields of linear algebra, the spectral theory of operators, operator algebras and, more broadly, functional analysis. Nonrelativistic
Mathematical_physics
Finite extension of the rationals
theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods. The notion of algebraic number field relies on the concept
Algebraic_number_field
Set of objects whose state must satisfy limits
algebra. It turned out that questions about the complexity of CSPs translate into important universal-algebraic questions about underlying algebras.
Constraint satisfaction problem
Constraint_satisfaction_problem
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
Freely generated algebraic structure over a given signature
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature
Term_algebra
Software for a class of mathematical problems
problems Systems of ordinary differential equations Systems of differential algebraic equations Boolean satisfiability problems, including SAT solvers Quantified
Solver
Study of categorified structures
higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra. A first
Higher-dimensional_algebra
Left adjoint to a forgetful functor to sets
concepts of abstract algebra. Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations
Free_object
Physical quantities taking values at each point in space and time
these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. spinors are not tensors, so may need calculus for spinor
Field_(physics)
Algebraic ring without a multiplicative identity
In abstract algebra, a rng (pronounced "rung" /rʌŋ/) or non-unital ring or pseudo-ring is an algebraic structure satisfying the same properties as a ring
Rng_(algebra)
Speech coding algorithm
coding (LPC) vocoders (e.g., FS-1015). Along with its variants, such as algebraic CELP, relaxed CELP, low-delay CELP and vector sum excited linear prediction
Code-excited linear prediction
Code-excited_linear_prediction
1960 article by Eugene Wigner
beauty”, nevertheless often find applications in physics. The mathematical structure of theoretical physics often points the way to further advances in that
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Study of abstract algebraic structures
In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital)
Algebra_representation
Mathematical set with some added structure
should be considered as a geometric "space", or an algebraic "structure". A general definition of "structure", proposed by Bourbaki, embraces all common types
Space_(mathematics)
Finite dimensional algebra over a field whose central elements are that field
areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative K-algebra A that is simple, and for which the center
Central_simple_algebra
Generalization of vector spaces from fields to rings
central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology. In a vector space, the
Module_(mathematics)
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
History_of_algebra
Reasoning about equations with free variables
and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics
Algebraic_logic
Algebraic structure used in theoretical physics
superalgebra is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into
Superalgebra
Methods of mathematical approximation
Examples of the "collection of equations" D {\displaystyle D} include algebraic equations, differential equations (e.g., the equations of motion and commonly
Perturbation_theory
topological algebra A {\displaystyle A} is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent
Topological_algebra
theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber
Gerstenhaber_algebra
Algebraic structure providing a semantics of Łukasiewicz logic
In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation ⊕ {\displaystyle \oplus } , a unary
MV-algebra
Formulation of classical mechanics using momenta
symplectic structure induces a Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra. If F and
Hamiltonian_mechanics
Algebra of 4D spacetime
name "algebra of physical space" (APS) originally stems from the use of the biquaternions via its definition as the real Clifford or geometric algebra Cl3
Algebra_of_physical_space
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
Surname or Lastname
English
English : variant of Pafford.
Female
English
Variant spelling of English Posy, POSEY means both "bouquet, flower" and "(God) shall add (another son)."
Female
English
English name derived from the name of the Mexican state or the Sonoran Desert, from Latin sonorus, SONORA means "clear, loud, resounding."
Girl/Female
Hindu, Indian
Blood; Small
Girl/Female
English American
Medieval English form of the Irish Caitlin. Pure.
Girl/Female
Bengali, Indian, Telugu
Powerful
Female
French
French form of Roman Latin Flavia, FLAVIE means "yellow hair."
Girl/Female
Christian, Hindu, Indian
Happiness
Female
Hebrew
(×™Ö¸×ָה) Hebrew name YAA means "beautiful." Compare with another form of Yaa.
Girl/Female
Tamil
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
STRUCTURABLE ALGEBRA
n.
Having the color spots, or structural parts, arranged spirally.
a.
Of or pertaining to structure; affecting structure; as, a structural error.
n.
The assumption of several structural forms without a corresponding difference in function; -- said of sponges, etc.
n.
A number of species or genera having certain structural characteristics in common; as, a tribe of plants; a tribe of animals.
a.
Fleshy; -- applied to the minute structural elements, called sarcous elements, or sarcous disks, of which striated muscular fiber is composed.
a.
Comprising structural characters which are separated in more specialized forms; synthetic; as, a generalized type.
n.
The syntactical or structural form peculiar to any language; the genius or cast of a language.
n.
An expression conforming or appropriate to the peculiar structural form of a language; in extend use, an expression sanctioned by usage, having a sense peculiar to itself and not agreeing with the logical sense of its structural form; also, the phrase forms peculiar to a particular author.
n.
Neuralgia of the kidneys; a disease characterized by pain in the region of the kidneys without any structural lesion of the latter.
n.
An affection characterized by pain in or about a joint, not dependent upon structural disease.
a.
Not capable of self-fertilization; -- said of hermaphrodite flowers in which some structural obstacle forbids autogamy.
n.
The classification of living organisms according to their structural character; taxonomy.
n.
A theoretical aggregation of molecules constituting a structural particle of protoplasm, capable of increase or diminution without change in chemical nature.
n.
A band; a structural line; -- applied to several bands and lines of nervous matter in the brain.
a.
Of or pertaining to organit structure; as, a structural element or cell; the structural peculiarities of an animal or a plant.
a.
Pertaining to an edifice; structural.
a.
A typical, structural unit; a type.
a.
Derived from epithelial cells and destined to become a part of the muscular system; -- applied to structural elements in certain embryonic forms.
a.
Pertaining to homology; having a structural affinity proceeding from, or base upon, that kind of relation termed homology.
v. t.
To determine the homologies or structural relations of.