SOME STUDIES ON GZI RINGS

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International Electronic Journal of Algebra
Volume:24 Issue:24
SOME STUDIES ON GZI RINGS

SOME STUDIES ON GZI RINGS

Authors : Yinchun QU, Junchao WEİ

Pages : 129-152

Doi:10.24330/ieja.440241

View : 13 | Download : 10

Publication Date : 2018-07-05

Article Type : Research Paper

Abstract :A ring R is called generalized ZI insert ignore into journalissuearticles values(or GZI for short); if for any a 2 Ninsert ignore into journalissuearticles values(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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