Module Theory
- General
- Module (mathematics)
- Bimodule
- Annihilator (ring theory)
- Structure
- Submodule
- Pure submodule
- Module homomorphism
- Essential submodule
- Superfluous submodule
- Singular submodule
- Socle of a module
- Radical of a module
- Constructions
- Free module
- Quotient module
- Direct sum, Direct product of modules
- Direct limit, Inverse limit
- Localization of a module
- Completion (ring theory)
- Types
- Simple module, Semisimple module
- Indecomposable module
- Artinian module, Noetherian module
- Homological types:
- Projective module
- Projective cover
- Swan's theorem
- Quillen–Suslin theorem
- Injective module
- Injective hull
- Flat module
- Flat cover
- Projective module
- Coherent module
- Finitely-generated module
- Finitely-presented module
- Finitely related module
- Algebraically compact module
- Reflexive module
- Concepts and theorems
- Composition series
- Length of a module
- Structure theorem for finitely generated modules over a principal ideal domain
- Homological dimension
- Projective dimension
- Injective dimension
- Flat dimension
- Global dimension
- Weak global dimension
- Cohomological dimension
- Krull dimension
- Regular sequence (algebra), depth (algebra)
- Fitting lemma
- Schur's lemma
- Nakayama's lemma
- Krull–Schmidt theorem
- Steinitz exchange lemma
- Jordan-Holder Theorem
- Artin–Rees lemma
- Schanuel's lemma
- Morita equivalence
- Progenerator
Read more about this topic: List Of Abstract Algebra Topics
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