Mehrdad Esfandiar - Department of Mathematics, Shahed University, Tehran, Iran
Hamid Haj Seyyed Javadi - Department of Computer Engineering, Shahed University, Tehran, Iran
Ahmad Moussavi - Department of Pure Mathematics, Tarbiat Modares, Tehran, Iran

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=۱ implies that ba=۱.

mj-clean ring, strongly mj-clean ring, Dedekind finite