Some Results of the Generalized Inverses of Module Homomorphisms
Feng Liang
Abstract
Feng Liang
Abstract
Let Ube an associative ring with 1,and M a left U-module.We consider the modules by the generalized inverses of homomorphisms,and we classify the modules with the regular inverses of homomorphisms.We make some necessary and sufficient conditions for a module to be direct injective,indecomposable,strongly indecomposable respectively.
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Let Ube an associative ring with 1,and M a left U-module.We consider the modules by the generalized inverses of homomorphisms,and we classify the modules with the regular inverses of homomorphisms.We make some necessary and sufficient conditions for a module to be direct injective,indecomposable,strongly indecomposable respectively.
Key concepts: Indecomposable module, Homomorphism, Injective module, Injective function, Associative property, Module, Mathematics, Ring (chemistry)