## Abelian categories with applications to rings and modules |

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An excellent book on Abelian categories and their applications to rings, modules and ideals.

Highly recommended.

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4-module 5-category abelian category abelian groups Ann(x artinian assertions are equivalent assume bijection canonical functor canonical inclusion canonical morphism Chapter cogenerator coirreducible subobject coker commutative diagram commutative ring contains Corollary covariant functor decomposition theory deduce defined denote direct product direct sum direct summand element epimorphism essential extension exact sequence Exercise finite type following assertions full subcategory Gabriel 59 Grothendieck category hence Homv(X hypothesis indecomposable injective inductive limit injective envelope injective object isomorphism kernel l.n.-category left ideal left prime Let F linearly compact localizing subcategory localizing system mapping module monomorphism Moreover natural number noetherian ring non-zero subobject Obviously ordinal preadditive category predecomposition theory prelocalizing system prime ideal projective Proof Proposition prove quotient object respectively right adjoint Section semi-artinian semisimple set of subobjects simple object special closed special open submodules spectral category structural morphisms subcategory of Mod subset Theorem topology two-sided ideal unique morphism