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2008•Jilin Normal University JournalRequires access

SR-projective Modules and SR-injective Modules

Xin Mou

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Abstract

By means of introducing semi-reflexive modules,we give the concept of SR-projective modules and SR-injective modules.And we also discuss their properties respectively.The properties of projective modules that keep direct sum,direct summand,extension and so on are generalized to SR-projective modules.According to dual property,we mainly discuss the properties of SR-injective modules,then we find the equivalence between the SR-injective modules and injective modules,so we get a new equivalent definition of injective modules.

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What this paper is about

By means of introducing semi-reflexive modules,we give the concept of SR-projective modules and SR-injective modules.And we also discuss their properties respectively.The properties of projective modules that keep direct sum,direct summand,extension and so on are generalized to SR-projective modules.According to dual property,we mainly discuss the properties of SR-injective modules,then we find the equivalence between the SR-injective modules and injective modules,so we get a new equivalent definition of injective modules.

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Available abstract

By means of introducing semi-reflexive modules,we give the concept of SR-projective modules and SR-injective modules.And we also discuss their properties respectively.The properties of projective modules that keep direct sum,direct summand,extension and so on are generalized to SR-projective modules.According to dual property,we mainly discuss the properties of SR-injective modules,then we find the equivalence between the SR-injective modules and injective modules,so we get a new equivalent definition of injective modules.

Key concepts: Injective function, Injective module, Projective module, Module, Mathematics, Projective cover, Flat module, Pure mathematics

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