Title of article :
SOME STUDIES ON GZI RINGS
Author/Authors :
Qu, Yinchun School of Mathematics - Yangzhou University, China , Wei, Junchao School of Mathematics - Yangzhou University, China
Abstract :
A ring R is called generalized ZI (or GZI for short) if for any
a ∈ N(R) and b ∈ R, ab = 0 implies aRba = 0, which is a proper generalization
of ZI rings. In this paper, many properties of GZI rings are introduced, some
known results are extended. Further, we introduce generalized GZI rings
as a generalization of GZI rings, and quasi-abel rings as a generalization of
generalized GZI rings. Some important results on Abel rings are extended to
generalized GZI rings and quasi-abel rings
Keywords :
ZI ring , GZI ring , quasi-abel ring , generalized GZI ring , reduced ring
Journal title :
International Electronic Journal of Algebra
