nil−INJECTIVE RINGS

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International Electronic Journal of Algebra
Volume:2 Issue:2
nil−INJECTIVE RINGS

nil−INJECTIVE RINGS

Authors : Junchao WEİ, Jianhua CHEN

Pages : 1-21

View : 13 | Download : 9

Publication Date : 2007-12-01

Article Type : Research Paper

Abstract :A ring R is called left nil-injective if every R-homomorphism from a principal left ideal which is generated by a nilpotent element to R is a right multiplication by an element of R. In this paper, we first introduce and characterize a left nil-injective ring, which is a proper generalization of left p-injective ring. Next, various properties of left nil-injective rings are developed, many of them extend known results.
Keywords : Left minimal elements, left min abel rings, strongly left min abel rings, left MC2 rings, simple singular modules, left nil injective modules

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