On generalizations of injective modules | Zendy

Burcu Nişancı Türkmen | Zendy

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On generalizations of injective modules

Author(s) -

Burcu Nişancı Türkmen

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim141215014t

Subject(s) - mathematics , injective function , ring (chemistry) , property (philosophy) , semisimple module , generalization , commutative ring , injective module , artinian ring , pure mathematics , primitive ring , principal ideal ring , noncommutative ring , discrete mathematics , commutative property , algebra over a field , mathematical analysis , noetherian , philosophy , chemistry , organic chemistry , epistemology

As a proper generalization of injective modules in term of supplements, we say that a module M has the property (SE) (respectively, the property (SSE)) if, whenever M ( N, M has a supplement that is a direct summand of N (respectively, a strong supplement in N). We show that a ring R is a left and right artinian serial ring with Rad(R)2 = 0 if and only if every left R-module has the property (SSE). We prove that a commutative ring R is an artinian serial ring if and only if every left R-module has the property (SE).

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