r-Clean Group Rings

Research Paper

Abstract

Let R be an associative ring with unity. An element a ∈ R is said to be r-clean if a = e + r, where e is an idempotent and r is a von Neumann regular element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we investigate the conditions under which the group ring RG is r-clean. We show that if R is a ring and G is a locally finite p-group with p ∈ J(R), then the group ring RG is r-clean if and only if R is r-clean.

Keywords

Clean rings Strongly J-clean rings Strongly J-clean group rings 

Mathematics Subject Classification

16S34 16Uxx 

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Copyright information

© Shiraz University 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematics, Statistics and Computer SciencesSemnan UniversitySemnanIran
  2. 2.Shahreza UniversityShahrezaIran

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