A note on mj-clean rings
نویسندگان
1 Department of Computer Engineering, Shahed University, Tehran, Iran.
2 Department of Mathematics, Shahed University, Tehran, Iran
3 Department of Pure Mathematics, Tarbiat Modares, Tehran, Iran
doi
10.22075/ijnaa.2023.30963.4528چکیده
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 $ba=1$.
