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Algebraic structure
appears in the theory of one-parameter operator semigroups: see C0-semigroup. The binary operation of a semigroup is most often denoted multiplicatively: x
Semigroup
mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup. Certain classes of E-semigroups have been studied
E-semigroup
In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse
E-dense_semigroup
Families of certain algebraic structures
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying
Special_classes_of_semigroups
Generalization of the exponential function
In mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function
C0-semigroup
Structure in group theory (in mathematics)
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse
Inverse_semigroup
Special kind of semigroup in mathematics
In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number
Numerical_semigroup
Action of a semigroup on a set
computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such
Semigroup_action
orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular E-semigroup
Orthodox_semigroup
In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such
Regular_semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of transformations (functions from a set to itself) that is closed under
Transformation_semigroup
refer to any topology on the semigroup. Let S be a semigroup and X a finite set of letters. A system of equations is a subset E of the Cartesian product X∗
Compact_semigroup
Mathematical structure that describes the dynamics in a Markovian open quantum system
Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups was first
Quantum_Markov_semigroup
linear or non-linear. Closely related to Markov operators is the Markov semigroup. The definition of Markov operators is not entirely consistent in the
Markov_operator
Semigroup with the cancellation property
In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the
Cancellative_semigroup
Algebraic structure with an associative operation and an identity element
with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of
Monoid
Generalization of additive and multiplicative inverses
an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regular semigroups; these are I-semigroups in which
Inverse_element
In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is
Bicyclic_semigroup
inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set
Symmetric_inverse_semigroup
continuous semigroups that gives a necessary and sufficient condition for a linear operator in a Banach space to generate a contraction semigroup. Let A be
Lumer–Phillips_theorem
Type of strongly continuous semigroup
In mathematics, an analytic semigroup is particular kind of strongly continuous semigroup. Analytic semigroups are used in the solution of partial differential
Analytic_semigroup
Theorem
continuous one-parameter semigroups of linear operators on Banach spaces. It is sometimes stated for the special case of contraction semigroups, with the general
Hille–Yosida_theorem
Approach to the study of finite semigroups and automata
finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and
Krohn–Rhodes_theory
Semigroup in abstract algebra
mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism
Semigroup_with_involution
American mathematician (1934–2011)
developing the theory of one-parameter semigroups of *-endomorphisms on von Neumann algebras - also known as E-semigroups. Among his achievements, he introduced
William_Arveson
Algebraic structure
mathematics, an ordered semigroup is a semigroup (S,•) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x
Ordered_semigroup
Set endowed with a partial binary operation
partial groupoid ( G , ∘ ) {\displaystyle (G,\circ )} is called a partial semigroup if the following associative law holds: For all x , y , z ∈ G {\displaystyle
Partial_groupoid
completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regular semigroups forms an important
Completely_regular_semigroup
Concept in mathematics
and semigroups. It follows that every monoid (or semigroup) arises as a homomorphic image of a free monoid (or semigroup). The study of semigroups as images
Free_monoid
presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of
Presentation_of_a_monoid
alphabet Σ, or as the induced transformation semigroup of Q. In older books like Clifford and Preston (1967) semigroup actions are called "operands". In category
Semiautomaton
Semigroup in which every element is idempotent
In mathematics, a band (also called idempotent semigroup) is a semigroup in which every element is idempotent (in other words equal to its own square)
Band_(algebra)
In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also
Brandt_semigroup
"numerical semigroup". A numerical semigroup is called an Arf semigroup if, for every three elements x, y, and z with z = min(x, y, and z), the semigroup also
Arf_semigroup
Algebraic structure in mathematics
mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen
Four-spiral_semigroup
Abstract algebra concept
{\displaystyle S} is a semigroup/monoid generating set of G {\displaystyle G} if G {\displaystyle G} is the smallest semigroup/monoid containing S {\displaystyle
Generating_set_of_a_group
Natural number
{\displaystyle a^{1}=a} , so that 1 is also the identity for any power semigroup. 1 is its own factorial 1 ! = 1 {\displaystyle 1!=1} . Moreover, the empty
1
relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named
Green's_relations
semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed
Rees_factor_semigroup
Type of semigroup
In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer
Aperiodic_semigroup
holomorphic univalent self-mappings of the unit disk, called a Loewner semigroup. This semigroup corresponds to a time dependent holomorphic vector field on the
Loewner_differential_equation
Clifford semigroup (sometimes also called "inverse Clifford semigroup") is a completely regular inverse semigroup. It is an inverse semigroup with x x
Clifford_semigroup
maximal cone. A similar decomposition already occurs in the semigroup. The oscillator semigroup of Roger Howe concerns the special case of this theory for
Invariant_convex_cone
Functional equation characterizing associative binary operations
associative in the usual algebraic sense, and therefore underlies the study of semigroups and many kinds of aggregation operators. When additional regularity conditions
Associativity_equation
Mathematical structure
In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating
Automatic_semigroup
Algebraic structure with a binary operation
the sense used by Hausmann and Ore. Nevertheless, influential books in semigroup theory, including Clifford and Preston (1961) and Howie (1995) use groupoid
Magma_(algebra)
Branch of mathematics
twentieth century. The fundamental notion involved is that of an arithmetic semigroup, which is a commutative monoid G satisfying the following properties:
Abstract analytic number theory
Abstract_analytic_number_theory
Theorem of dominion in abstract algebra
American mathematician John R. Isbell in 1966. Dominion is a concept in semigroup theory, within the study of the properties of epimorphisms. For example
Isbell's_zigzag_theorem
Stochastic process
sup norm is a Banach space. A Feller semigroup on C 0 ( X ) {\textstyle C_{0}(X)} is a contraction C0-semigroup of positive operators on C 0 ( X ) {\textstyle
Feller_process
an abstract Cauchy problem one can associate a semigroup of operators U ( t ) {\displaystyle U(t)} , i.e. a family of bounded linear operators depending
Abstract differential equation
Abstract_differential_equation
Example of a Semigroup
a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having
Semigroup_with_two_elements
Type of semigroup
quasi-periodic semigroup, group-bound semigroup, completely π-regular semigroup, strongly π-regular semigroup (sπr), or just π-regular semigroup (although
Epigroup
every element has a weak inverse, the semigroup is called an E-inversive or E-dense semigroup. An E-inversive semigroup may equivalently be defined by requiring
Weak_inverse
principal factor of a J {\displaystyle {\mathcal {J}}} -class J of a semigroup S is equal to J if J is the kernel of S, and to J ∪ { 0 } {\displaystyle
Principal_factor
mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents)
Munn_semigroup
In mathematics, a topological semigroup is a semigroup that is simultaneously a topological space, and whose semigroup operation is continuous. Every topological
Topological_semigroup
Function that applies a set to itself
function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention
Transformation_(function)
Bounded operators with sub-unit norm
= e A t , {\displaystyle \displaystyle {T(t)=e^{At},}} in the sense of the spectral theorem and this notation is used more generally in semigroup theory
Contraction_(operator_theory)
representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the complex numbers into itself. Let
Koenigs_function
Mathematical group
regular semigroup discovered by K S S Nambooripad in late seventies. Since the same partial order was also independently discovered by Robert E Hartwig
Nambooripad_order
Special type of element of a set
element with any element of the set is the absorbing element itself. In semigroup theory, the absorbing element is called a zero element because there is
Absorbing_element
Mathematical structure with greatest common divisors
GCD-semigroup. A GCD-semigroup is a semigroup with the additional property that for any a {\displaystyle a} and b {\displaystyle b} in the semigroup S {\displaystyle
GCD_domain
idempotents in a semigroup. The set of idempotents in a semigroup is a biordered set and every biordered set is the set of idempotents of some semigroup. A regular
Biordered_set
Generalized function whose value is zero everywhere except at zero
convolution semigroups arising from such a fundamental solution include the following. The heat kernel, defined by η ε ( x ) = 1 2 π ε e − x 2 2 ε {\displaystyle
Dirac_delta_function
Theorem in convex and algebraic geometry
(this follows from the fact that the prime spectrum of the semigroup algebra of such a semigroup is, by definition, an affine toric variety). The lemma is
Gordan's_lemma
Differential operator in mathematics
functional calculus: for example, the heat semigroup corresponds to multiplication by e − 4 π 2 t | ξ | 2 , {\displaystyle e^{-4\pi ^{2}t|\xi |^{2}},} and, more
Laplace_operator
Set with operations obeying given axioms
identity element if there is an element e such that x ∗ e = x and e ∗ x = x {\displaystyle x*e=x\quad {\text{and}}\quad e*x=x} for all x in the structure. Here
Algebraic_structure
American mathematician
finite inverse semigroups was supervised by Mario Petrich [wd] (1932–2015), famous among mathematicians for his research in semigroup theory. From 1970
David_E._Zitarelli
measurable, when each of the individual operators is strongly measurable. A semigroup of linear operators can be strongly measurable yet not strongly continuous
Strongly_measurable_function
American mathematician (1908–1992)
Louis, Missouri who is known for Clifford theory and for his work on semigroups. He did his undergraduate studies at Yale and his PhD at Caltech, and
Alfred_H._Clifford
Special types of subgroups encountered in group theory
apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the multiplication of the ring (a semigroup operation)
Centralizer_and_normalizer
Algorithm for fast exponentiation
positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred
Exponentiation_by_squaring
Generalization of strings in computer science
stable under the monoid operation on Σ ∗ {\displaystyle \Sigma ^{*}} , i.e., concatenation, and ≡ D {\displaystyle \equiv _{D}} is therefore a congruence
Trace_monoid
Indian mathematician (1935–2020)
who made fundamental contributions to the structure theory of regular semigroups. Nambooripad was also instrumental in popularising the TeX software in
K._S._S._Nambooripad
arXiv:math.CO/0001078. Arveson, William (2003), Noncommutative dynamics and E-semigroups, New York: Springer, ISBN 0-387-00151-4. Tsirelson, Boris (2003), "Non-isomorphic
List of probabilistic proofs of non-probabilistic theorems
List_of_probabilistic_proofs_of_non-probabilistic_theorems
Set of natural numbers
extended from subsets of the special semigroup of natural numbers with addition to subsets of semigroups and partial semigroups in general. A variant of Hindman's
IP_set
Mathematical category formed by reversing morphisms
Given a semigroup (S, ·), one usually defines the opposite semigroup as (S, ·)op = (S, *) where x*y ≔ y·x for all x,y in S. So also for semigroups there
Opposite_category
Representation theory of the symplectic group
representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been
Oscillator_representation
English mathematician (1925–2015)
14 April 2015) was an English mathematician best known for his work on semigroups. He received his D.Phil. in mathematics in 1954 from Magdalen College
Gordon_Preston
Concept in abstract algebra
the context. A classic result in semigroup theory due to D. B. McAlister states that every inverse semigroup has an E-unitary cover; besides being surjective
Cover_(algebra)
Smallest monoid that recognizes a formal language
ISBN 1-58488-255-7. Zbl 1086.68074. Pin, Jean-Éric (1997). "10. Syntactic semigroups". In Rozenberg, G.; Salomaa, A. (eds.). Handbook of Formal Language Theory
Syntactic_monoid
Markovian quantum master equation for density matrices (mixed states)
for various times are collectively referred to as a quantum dynamical semigroup—a family of quantum dynamical maps ϕ t {\displaystyle \phi _{t}} on the
Lindbladian
Operation in group theory
at least P.) In a semigroup S, the product of two subsets defines a structure of a semigroup on P(S), the power set of the semigroup S; furthermore P(S)
Product_of_group_subsets
Branch of mathematics
specialized structure by adding constraints. For example, a magma becomes a semigroup if its operation is associative. Homomorphisms are tools to examine structural
Algebra
direct product of a right zero semigroup and a group, while a right abelian group is the direct product of a right zero semigroup and an abelian group. Left
Right_group
Property of a binary operation
alternative is said to be alternative. Any associative magma (that is, a semigroup) is alternative. More generally, a magma in which every pair of elements
Alternativity
Algorithmic process of solving equations
has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative. But the same problem, viewed in an
Unification (computer science)
Unification_(computer_science)
Operator in analysis and probability theory
E , μ ) {\displaystyle (X,{\mathcal {E}},\mu )} be a σ-finite measure space, { P t } t ≥ 0 {\displaystyle \{P_{t}\}_{t\geq 0}} a Markov semigroup of
Carré_du_champ_operator
Function whose actual domain of definition may be smaller than its apparent domain
{\displaystyle X,} forms a regular semigroup called the semigroup of all partial transformations (or the partial transformation semigroup on X {\displaystyle X} )
Partial_function
Type of vector space in math
states the following: If Ut is a (strongly continuous) one-parameter semigroup of unitary operators on a Hilbert space H, and P is the orthogonal projection
Hilbert_space
Algebraic structure
bi-commutative, bisymmetric, surcommutative, entropic, etc. Any commutative semigroup is a medial magma, and a medial magma has an identity element if and only
Medial_magma
Soviet-born Israeli mathematician (1944–2024)
for semigroups of order less than six. Semigroup Forum, 27(1983), 387-389. A.N. Trahtman. Finiteness of a basis of identities of 5-element semigroups. Polugruppy
Avraham_Trahtman
Probabilistic problem-solving algorithm
Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups". ESAIM Probability & Statistics. 7: 171–208. doi:10.1051/ps:2003001.
Monte_Carlo_method
Overview of and topical guide to algebraic structures
groupoid: S and a single binary operation over S. Semigroup: an associative magma. Monoid: a semigroup with identity element. Group: a monoid with a unary
Outline of algebraic structures
Outline_of_algebraic_structures
Open problem on 3x+1 and x/2 functions
portal Wikimedia Commons has media related to Collatz conjecture. 3x + 1 semigroup Arithmetic dynamics Juggler sequence Modular arithmetic Residue-class-wise
Collatz_conjecture
partitions of 12 white objects and 3 black ones 1915 = number of nonisomorphic semigroups of order 5 1916 = sum of first 50 composite numbers 1917 = number of partitions
1000_(number)
Type of algebraic structure
Remarks: If we do not require that the ring have an identity element, semigroups may replace monoids. Examples: A group naturally grades the corresponding
Graded_ring
Algebraic structure with a ternary operation
biunitary element e may be considered an involuted semigroup with operation given by ab = [a, e, b] and involution by a–1 = [e, a, e]. When the above construction
Heap_(mathematics)
compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of K {\displaystyle K} has at least one fixed point
Ryll-Nardzewski fixed-point theorem
Ryll-Nardzewski_fixed-point_theorem
Algebra describing information processing
, D ) {\displaystyle (\Phi ,D)} : Where Φ {\displaystyle \Phi } is a semigroup, representing combination or aggregation of information, and D {\displaystyle
Information_algebra
E SEMIGROUP
E SEMIGROUP
Female
French
French name, derived from the French word aimée, AIMÉE means "much loved."
Boy/Male
American, British, English
Birch
Female
French
Feminine form of French unisex Esmé, ESMÉE means "esteemed, loved."
Girl/Female
French, German, Latin
Virgin
Female
French
French form of Latin Medea, MÉDÉE means "cunning."
Female
French
Feminine form of French Honoré, HONORÉE means "honor, valor."
Female
French
Feminine form of French Iréné, IRÉNÉE means "peaceful."
Female
French
French form of Latin Dorothea, DOROTHÉE means "gift of God."
Female
French
French feminine form of Latin Josephus, JOSÉE means "(God) shall add (another son)."Â
Female
French
Feminine form of French René, RENÉE means "reborn."
Female
French
Pet form of French Estelle, ESTÉE means "star."
Boy/Male
American, British, English
Bird
Girl/Female
French, German, Latin, Spanish
Modest
Male
Slovene
Pet form of Slovene Jožef, JOŽE means "(God) shall add (another son)."Â
Female
French
Feminine form of French Désiré, DÉSIRÉE means "desired."Â
Female
French
Feminine form of French Dieudonné, DIEUDONNÉE means "God-given."
Male
French
French form of Latin Isaias, ISAÃE means "God is salvation."
Boy/Male
English, Modern
A Miracle; Inimitably; Do Something which Others cannot do
Female
French
Feminine form of French André, ANDRÉE means "man; warrior."
Male
French
French form of Latin Timotheus, TIMOTHÉE means "to honor God."
E SEMIGROUP
E SEMIGROUP
Girl/Female
Hindu, Indian
Good
Surname or Lastname
Romanian
Romanian : from the personal name Marian, from Latin Marianus (see Mariano).English and French : from a pet form of Marie.
Biblical
God hearing
Girl/Female
Hebrew American Hungarian Greek English
or Elizabeth, from Elisheba, meaning either oath of God, or God is satisfaction. Also a...
Girl/Female
Indian
Kind to people
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sikh, Telugu, Traditional
Servant of the Guru
Female
Italian
Italian and Spanish form of French Noëlle, NOELIA means "day of birth."
Girl/Female
Hindu, Indian, Turkish
A Flower-jasmine
Boy/Male
Arabic, Indian, Muslim
Kuran; Revelation; Sending Down
Boy/Male
Australian, French, Hebrew, Irish, Scottish
From the Headland
E SEMIGROUP
E SEMIGROUP
E SEMIGROUP
E SEMIGROUP
E SEMIGROUP
n.
See Elevator, n. (e).
e. i.
To cut with a grating sound; to cut; to penetrate or pierce harshly; as, the griding sword.
e. t.
To make cool.
a.
Covered with a mant/e; cloaked; disguised.
superl.
Not decidedly marked; not forcible; inconsiderable; unimportant; insignificant; not severe; weak; gentle; -- applied in a great variety of circumstances; as, a slight (i. e., feeble) effort; a slight (i. e., perishable) structure; a slight (i. e., not deep) impression; a slight (i. e., not convincing) argument; a slight (i. e., not thorough) examination; slight (i. e., not severe) pain, and the like.
e
(imp.) of Wit
n.
See Set, n., 2 (e) and 3.
v. t.
To liken; to compa/e.
a.
Bold; brave; stout; daring; resolu?e; intrepid.
a.
Lower by a semitone; flat; as, E molle, that is, E flat.
a.
Old; as, Auld Reekie (old smoky), i. e., Edinburgh.
n.
A female pope; i. e., the fictitious pope Joan.
superl.
Possessing a characteristic quality in a supreme or superior degree; as, high (i. e., intense) heat; high (i. e., full or quite) noon; high (i. e., rich or spicy) seasoning; high (i. e., complete) pleasure; high (i. e., deep or vivid) color; high (i. e., extensive, thorough) scholarship, etc.
n.
An evergreen shrub of the genus Erica (E. passerina).
n.
Originally, the highest note in the scale of Guido; hence, proverbially, any extravagant saying.
pl.
of Notopodium