Rings and Categories of Modules |
Contents
Preface 0 Preliminaries | 1 |
Rings Modules and Homomorphisms | 10 |
2 Modules and Submodules | 26 |
Copyright | |
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a₁ abelian group algebra annihilator artinian ring BiEnd(RM bimodule commutative complements direct summands composition series Corollary decomposition that complements defined diagram direct sum direct summand division ring dual e₁ element End(RM endomorphism ring epic epimorphism exact sequence Exercise factor module faithful finitely cogenerated finitely generated projective following are equivalent functors Hint Homg HomŔ(M idempotents indecomposable decomposition indexed set injective envelope injective modules inverse K₁ lattice left artinian left ideal left noetherian Lemma M₁ M₂ matrices maximal submodule minimal monic monomorphism Morita duality morphism N₁ nilpotent orthogonal primitive idempotents primitive ring projective cover projective module Proof Proposition Prove quasi-regular R-homomorphism R₁ Re₁ right artinian right R-module ring and let ring homomorphism semiperfect ring serial ring simple left R-module simple modules subring subset Suppose Theorem U-reflexive u₁ unique vector space