IJPAM: Volume 77, No. 5 (2012)

SPQ-INJECTIVE MODULES AND SQP-INJECTIVE MODULES

Zhu Zhanmin
Department of Mathematics
Jiaxing University
Jiaxing, Zhejiang Province, 314001, P.R. CHINA


Abstract. Let $R$ be a ring. A right $R$-module $M$ is called simple principally quasi -injective (briefly SPQ-injective) if, every $R$-homomorphism from a principal submodule of $M$ to $M$ with simple image extends to an endomorphism of $M$. A right $R$-module $M$ is called simple quasi-principally injective (briefly SQP-injective) if, every $R$-homomorphism from an $M$-cyclic submodule of $M$ to $M$ with simple image extends to an endomorphism of $M$. SPQ-injective modules and SQP-injective modules with some Kasch conditions are investigated, and minimal quasi-injective modules are also investigated, some results on right principally injective rings obtained by Weimin Xue are improved.

Received: September 29, 2011

AMS Subject Classification: 16D50, 16D60, 16L30

Key Words and Phrases: SPQ-injective modules, SQP-injective modules, Kasch modules, weakly Kasch modules, strongly Kasch modules

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 5