Duality in the Category of Modules: Applications |
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56 Seiten A₁ artinian modules Bodo Pareigis cocyclic quotient module cofree coindependent family coindependent submodules complemented projective R-module CorankM CorankM/K Corollary cosum direct sum direct summand DM 9 dual notion dual properties dual statements dualizable Endomorphism rings epimorphism essential submodule exact sequence family of coindependent family of quotient family of submodules finite corank finitely cogenerated follows Günter Hauger Helmut Zöschinger Hence hereditary rings homomorphism f implies inclusion map injective cogenerator injective R-module intersection isomorphism Kerf Kerp left hereditary left ideal left perfect lemma maximal member maximal submodule minimal complement modular law monomorphism München N₁ N₂ noetherian noetherian module non-zero R-module phism Proof proper submodule quotient module M/N R-module homomorphism R-module is injective R-module is projective rule S₁ semi-simple Si,n simple R-module simple submodule statement in R-mod statement involving strongly complemented projective superfluous submodule terms of submodules Theorem Toma Albu U₁ Universal Algebra V₁ Wischnewsky Wolfgang Zimmermann zero R-module