Weakly np-Injective Rings and Weakly C2 Rings

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 1,  2011, pp.93-108
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.1.093
Title & Authors
Weakly np-Injective Rings and Weakly C2 Rings
Wei, Junchao; Che, Jianhua;

Abstract
A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $\small{Ra^n}$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $\small{_RR}$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.
Keywords
Left weakly np- injective rings;Left weakly C2 rings;Directly finite rings;Regular rings;
Language
English
Cited by
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