Definition of Submodule. Meaning of Submodule. Synonyms of Submodule

Here you will find one or more explanations in English for the word Submodule. Also in the bottom left of the page several parts of wikipedia pages related to the word Submodule and, of course, Submodule synonyms and on the right images related to the word Submodule.

Definition of Submodule

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Meaning of Submodule from wikipedia

- condition on submodules, that is, every increasing chain of submodules becomes stationary after finitely many steps. Equivalently, every submodule is finitely...
- mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved...
- 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...
- let S and T be submodules of M. Then: The sum S + T = {s + t | s ∈ S, t ∈ T} is a submodule of M, The intersection S ∩ T is a submodule of M, and The quotient...
- For an R-module A, a maximal submodule M of A is a submodule M ≠ A satisfying the property that for any other submodule N, M ⊆ N ⊆ A implies N = M or...
- 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...
- ring. The torsion submodule of a module is the submodule formed by the torsion elements (in cases when this is indeed a submodule, such as when the ring...
- and module theory, each right (resp. left) R-module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left)...
- stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules. This contains the case...
- nonzero submodules of M. It can be considered as a dual notion to that of the radical of a module. In set notation, soc(M)=∑N is a simple submodule of MN...