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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
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
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
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
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
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)
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
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)
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)
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
*-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
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
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
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DENSE SUBMODULE
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