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On Semi π-Regular Local Ring

DOI: 10.4236/oalib.1104788, PP. 1-7

Subject Areas: Algebra

Keywords: Local, Ring, Semi π-Regular

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Abstract

A ring R is said to be a right (left) semi π-regular local ring if and only if for all a in R, either a or (1-a) is a right (left) semi π-regular element. The purpose of this paper is to give some characterization and properties of semi π-regular local rings, and to study the relation between semi π-regular local rings and local rings. From the main results of this work: 1) Let R be a semi π-regular reduced ring. Then the idempotent associated element is unique. 2) Let R be a ring. Then R is a right semi π-regular local ring if and only if either r(an) or r((1-a)n) is direct summand for all aR and nZ . If R is a local ring with r(anr(a) for all aR and nZ , then R is a right semi π-regular local ring.

Cite this paper

Ibraheem, Z. M. , Mustafa, R. A. and Khalf, M. F. (2018). On Semi π-Regular Local Ring. Open Access Library Journal, 5, e4788. doi: http://dx.doi.org/10.4236/oalib.1104788.

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