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arXiv · 1607.07924

SS-Injective Modules and Rings

Adel Salim Tayyah·Akeel Ramadan Mehdi
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Abstract

We introduce and investigate ss-injectivity as a generalization of both soc-injectivity and small injectivity. A module M is said to be ss-N-injective (where N is a module) if every R-homomorphism from a semisimple small submodule of N into M extends to N. A module M is said to be ss-injective (resp. strongly ss-injective), if M is ss-R-injective (resp. ss-N-injective for every right R-module N). Some characterizations and properties of (strongly) ss-injective modules and rings are given. Some results of Amin, Yuosif and Zeyada on soc-injectivity are extended to ss-injectivity. Also, we provide some new characterizations of universally mininjective rings, quasi-Frobenius rings, Artinian rings and semisimple rings.

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Adel Salim Tayyah, Akeel Ramadan Mehdi. 2016-07-27. SS-Injective Modules and Rings. https://arxiv.org/abs/1607.07924

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