Principally Small Injective Rings | Zendy

Yueming Xiang | Zendy

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Principally Small Injective Rings

Author(s) -

Yueming Xiang

Publication year - 2011

Publication title -

kyungpook mathematical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.287

H-Index - 19

eISSN - 1225-6951

pISSN - 0454-8124

DOI - 10.5666/kmj.2011.51.2.177

Subject(s) - annihilator , mathematics , ideal (ethics) , jacobson radical , injective function , minimal ideal , ring (chemistry) , radical of a ring , principal ideal ring , combinatorics , associated prime , pure mathematics , maximal ideal , discrete mathematics , commutative ring , algebra over a field , prime (order theory) , commutative property , chemistry , law , organic chemistry , political science

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I 6= R. A right R-module M is called PS-injective if every R-homomorphism f: aR ! M for every principally small right ideal aR can be extended to R ! M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

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