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...

M with a submodule N, the module M is said to be an essential extension of N (or N is said to be an essential submodule or large submodule of M) if for...

exist in a graph Dense order in order theory A coinitial subset in the mathematical theory of forcing, in set theory Dense submodule in abstract algebra...

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...

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...

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...

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...

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...

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...

vector space of finite dimension which is a G-module, its G-submodules and K-submodules are the same. In the Encyclopedia of Mathematics, the formulation...

ring. Von Neumann algebras are semihereditary: every finitely generated submodule of a projective module is itself projective. There have been several attempts...

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...

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...

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...

{C}}\Omega ^{i}({\mathcal {O}})\subseteq \Omega ({\mathcal {O}})} be the submodule of differential forms over O {\displaystyle {\mathcal {O}}} whose restriction...

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...

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...