maximal submodule

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• Maximal ideal — In mathematics, more specifically in ring theory, a maximal ideal is an ideal which is maximal (with respect to set inclusion) amongst all proper ideals.[1][2] In other words, I is a maximal ideal of a ring R if I is an ideal of R, I ≠ R, and… …   Wikipedia

• Dense submodule — In abstract algebra, specifically 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 also be said it may alternatively be said that N ⊆ M is a… …   Wikipedia

• Singular submodule — In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is… …   Wikipedia

• Nakayama lemma — In mathematics, more specifically modern algebra and commutative algebra, Nakayama s lemma also known as the Krull–Azumaya theorem[1] governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely… …   Wikipedia

• Radical of a module — In mathematics, in the theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for rings. In many ways, it is the dual notion to that of the socle… …   Wikipedia

• Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… …   Wikipedia

• Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… …   Wikipedia

• Serial module — Chain ring redirects here. For the bicycle part, see Chainring. In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M,… …   Wikipedia

• Essential extension — In mathematics, specifically module theory, given a ring R and R modules :Msubseteq E, the module E is an essential extension if for every nonzero submodule :Nsubseteq E, we have:Ncap M e 0. Also, M is then said to be an essential submodule of E …   Wikipedia

• Composition series — In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many… …   Wikipedia

• Verma module — Verma modules, named after Daya Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics. The definition of a Verma module looks complicated, but Verma modules are very natural objects, with useful properties …   Wikipedia