IJPAM: Volume 77, No. 5 (2012)
Department of Mathematics
Jiaxing, Zhejiang Province, 314001, P.R. CHINA
Abstract. Let be a ring. A right -module is called simple principally quasi -injective (briefly SPQ-injective) if, every -homomorphism from a principal submodule of to with simple image extends to an endomorphism of . A right -module is called simple quasi-principally injective (briefly SQP-injective) if, every -homomorphism from an -cyclic submodule of to with simple image extends to an endomorphism of . 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