International Journal of Nonlinear Analysis and Applications

A note on mj-clean rings

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahed University, Tehran, Iran

2 Department of Computer Engineering, Shahed University, Tehran, Iran

3 Department of Pure Mathematics, Tarbiat Modares, Tehran, Iran

Abstract

In this paper, we examine the notions of $mj$-clean ring and strongly $mj$-clean ring. And we will provide some of its basic properties. We examine the relationship of $mj$-clean ring with $m$-clean ring and $j$-clean ring. We prove that $R$  is strongly $mj$-clean ring if and only if $M_n(R)$ is strongly $mj$-clean ring. We prove that $mj$-clean ring is Dedekind-finite; i.e., $ab=1$ implies that $ba=1$.    

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 10
October 2024
Pages 175-179
  • Receive Date: 15 June 2023
  • Accept Date: 23 September 2023