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in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may alternatively
Dense_submodule
Concept in mathematics
essential submodule is that of superfluous submodule (or small submodule). A submodule N {\displaystyle N} is superfluous if for any other submodule H {\displaystyle
Essential_extension
a module is a way to express a module as a direct sum of submodules. dense dense submodule determinant The determinant of a finite free module over a
Glossary_of_module_theory
which moreover coincides with the topology induced from A, and that B is dense in A. Picking a generator in each cyclic direct summand of B creates a p-basis
Basic_subgroup
Mathematical theorem in representation theory
U} is a B-submodule if and only if it is invariant under GL ( V ) {\displaystyle \operatorname {GL} (V)} ; in other words, a B-submodule is the same
Schur–Weyl_duality
Algebraic structure
completely reducible) if it is the direct sum of simple (irreducible) submodules. A ring is said to be (left)-semisimple if it is semisimple as a left
Noncommutative_ring
Mathematical theorem
If u is a non-zero element of U, u • R = U (where u • R is the cyclic submodule of U generated by u). Therefore, if u, v are non-zero elements of U, there
Jacobson_density_theorem
In linear algebra, generated subspace
with the case of vector spaces, the submodule of A spanned by any subset of A is the intersection of all submodules containing that subset. In functional
Linear_span
Project in integrated circuit design
IP blocks and submodules may be stored and referenced. OpenDB offers a method for adding custom data to objects using sparse or dense attributes. This
OpenROAD_Project
Set whose pairs have minima and maxima
distributive lattices, examples of modular lattices are the lattice of submodules of a module (hence modular), the lattice of two-sided ideals of a ring
Lattice_(order)
*-algebra of bounded operators on a Hilbert space
ring. Von Neumann algebras are semihereditary: every finitely generated submodule of a projective module is itself projective. There have been several attempts
Von_Neumann_algebra
Concept in mathematics
dominant weight λ, the irreducible representation L(λ) is the unique simple submodule (the socle) of the Schur module ∇(λ), but it need not be equal to the
Reductive_group
Nonempty, upper-bounded, downward-closed subset
(mathematics) – Special subset of a partially ordered set Ideal (ring theory) – Submodule of a mathematical ring Ideal on a set – Non-empty family of sets that
Ideal_(order_theory)
Special subset of a partially ordered set
Cartan 1937b. Bumby, R. T. (1965-12-01). "Modules which are isomorphic to submodules of each other". Archiv der Mathematik. 16 (1): 184–185. doi:10.1007/BF01220018
Filter_(mathematics)
Device in the representation theory of Lie groups
vector space of finite dimension which is a G-module, its G-submodules and K-submodules are the same.[clarification needed] In the Encyclopedia of Mathematics
Unitarian_trick
Algebraic construct of interest in theoretical physics
of a tensor product of highest weight modules, its decomposition into submodules is the same as for the tensor product of the corresponding modules of
Quantum_group
Differential variety
{C}}\Omega ^{i}({\mathcal {O}})\subseteq \Omega ({\mathcal {O}})} be the submodule of differential forms over O {\displaystyle {\mathcal {O}}} whose restriction
Diffiety
allows for the module-theoretic terminology: e.g., trivial G-module, G-submodules, etc. G-equivariant vector bundle A G-equivariant vector bundle is a vector
Glossary of representation theory
Glossary_of_representation_theory
DENSE SUBMODULE
DENSE SUBMODULE
Boy/Male
English
From the valley.
Surname or Lastname
English (Kent)
English (Kent) : variant spelling of Denn.
Male
English
Variant spelling of English Dean, DENE means "dean, ecclesiastical supervisor."
Surname or Lastname
English
English : ethnic name for someone from Denmark, from Middle English den(s)ch ‘Danish’ (Old English denisc). There were many Danes in England in the Middle Ages, not only the long-established settlers in the Danelaw region, but also more recent immigrants.
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Indian, Portuguese, Swedish, Swiss
God of Wine; Feminine of Dennis; To Advise; Alone; Nun; Solitary; Follower of Dionysus
Girl/Female
American, Australian, French, Greek
Mountain of Zeus; Feminine of Dennis; Follower of Dionysius
Girl/Female
Christian & English(British/American/Australian)
Form of Dennis
Female
English
Feminine form French Denis, DENISE means "follower of Dionysos."
Girl/Female
American, Australian, British, English, Greek
Combination of Deana and Dina
Boy/Male
Australian, German, Greek, Hungarian
God of Wine; Wine; Drama; Follower of Dionysus
Girl/Female
Australian, Greek
The Mythological Mother of Perseus by Zeus; Form of Danae
Girl/Female
Hindu, Indian
People who Give
Girl/Female
Indian
Boy/Male
Christian, Indian
From Dionysisu; God of Wine
Girl/Female
English American French
From the Latin Dionysos or Dionysus, referring to the Greek god of wine.
Girl/Female
French
Feminine of Denis from the Greek name Dionysus.
Girl/Female
English
Combination of Deana (divine) and Dina (from the valley; avenged).
Boy/Male
American, Anglo, Australian, British, Christian, English
From the Valley; Place Name; Valley; Occupational Name; Church Official
Boy/Male
Greek
God of wine.
Girl/Female
Greek
Form of Danae; the mythological mother of Perseus by Zeus.
DENSE SUBMODULE
DENSE SUBMODULE
Girl/Female
Indian
Daughter
Female
English
Variant spelling of English Aeryn, AERYNN means "Ireland."
Boy/Male
Indian
True Lover
Girl/Female
Muslim/Islamic
Town in Makkah where the pilgrims used to dorn their ehrams
Girl/Female
Muslim/Islamic
Kindness benefaction, bestowal
Surname or Lastname
English
English : habitational name from Ghent in Flanders, from which many wool workers and other skilled craftsmen migrated to England in the early Middle Ages. The surname is found most commonly in West Yorkshire, around Leeds. The Flemish place name is first recorded in Latin documents as Gandi and Gandavum; it is apparently of Celtic origin, but of uncertain meaning.English : from a nickname from Middle English gaunt ‘thin’, ‘wasted’, ‘haggard’ (of uncertain, possibly Scandinavian, origin).English : variant of Gant.
Girl/Female
Hindu, Indian, Tamil
Intelligent
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : topographic name for someone dwelling ‘at the enclosure’, Middle English atte hey (from Old English (ge)hæg ‘enclosure’).Irish : variant of Athy.
Boy/Male
Assamese, Indian
Sining
Girl/Female
Arabic, Australian, Christian, Indian, Kannada, Muslim
Blessing
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
DENSE SUBMODULE
n.
A census; -- also, a public rate or tax.
v. i.
To burn or scatter incense.
a.
Stupid; gross; crass; as, dense ignorance.
v. t.
Perception through the intellect; apprehension; recognition; understanding; discernment; appreciation.
n.
Condition; rank.
v. t.
A faculty, possessed by animals, of perceiving external objects by means of impressions made upon certain organs (sensory or sense organs) of the body, or of perceiving changes in the condition of the body; as, the senses of sight, smell, hearing, taste, and touch. See Muscular sense, under Muscular, and Temperature sense, under Temperature.
v. t.
That which is felt or is held as a sentiment, view, or opinion; judgment; notion; opinion.
v. t.
One of two opposite directions in which a line, surface, or volume, may be supposed to be described by the motion of a point, line, or surface.
a.
Having the constituent parts massed or crowded together; close; compact; thick; containing much matter in a small space; heavy; opaque; as, a dense crowd; a dense forest; a dense fog.
v. t.
Moral perception or appreciation.
v. t.
Sound perception and reasoning; correct judgment; good mental capacity; understanding; also, that which is sound, true, or reasonable; rational meaning.
v. t.
Meaning; import; signification; as, the true sense of words or phrases; the sense of a remark.
v. t.
Perception by the sensory organs of the body; sensation; sensibility; feeling.
n.
One of the forms which a verb takes by inflection or by adding auxiliary words, so as to indicate the time of the action or event signified; the modification which verbs undergo for the indication of time.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
v. t.
To perceive by the senses; to recognize.
v. t.
To perfume with odors from burning gums and spices.
n.
Manliness; dignity; comeliness; civility.
v. t.
To grace.