SOME STUDIES ON GZI RINGS

Year 2018, Volume: 24 Issue: 24, 129 - 152, 05.07.2018

Yinchun Qu Junchao Wei

https://doi.org/10.24330/ieja.440241

Abstract

A ring R is called generalized ZI (or GZI for short) if for any

a 2 N(R) and b 2 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

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