Commuting $\pi$-regular rings

Subject Areas : Rings theory

Sh. Sahebi ¹ (Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran)
M. Azadi ² (Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran)

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-06-01

Keywords: Regular, Commuting $\pi$-regular,

Abstract :

R is called commuting regular ring (resp. semigroup) if for each x,y $\in$ R thereexists a $\in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $\pi$-regular rings (resp. semigroups) and study various properties of them.

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