Commuting $\pi$-regular rings

محورهای موضوعی : Rings theory

Sh. Sahebi ¹ , M. Azadi ²

1 - Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran
2 - Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran

تاریخ دریافت : 1391/10/12 تاریخ پذیرش : 1391/10/12 تاریخ انتشار : 1392/03/11

کلید واژه: Regular, Commuting $\pi$-regular,

چکیده مقاله :

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.

منابع و مأخذ:

[1] M. Azadi, H. Doostie, L. Pourfaraj, Certain rings and semigroups examining the regularity property, Journal of mathematics, statistics and allied elds., 29(2008), 1:1-6.
[2] J. W. Fisher, R. L. Snider, On the Von Neumann regularity of rings with regular prime factor rings, Pacific J. Math., 54(1974),1: 135-144.
[3] H. Doostie, L. Pourfaraj, On the minimal of commuting regular rings and semigroups, Intarnal, J. Appl. Math. 19(2006), 2: 201-216.
[4] J. M. Howie, Fundamentals of semigroup Theory, Clarendon Press. Oxford, New York (1995).
[5] Sh. A. Safari Sabet, Commutativity conditions for rings with unity, Internal. J. Appl. Math. 15 (2004), 9-15.
[6] A. H. Yamini, Sh. A. Safari Sabet, Commuting regular rings, Internal. J. Appl. Math. 14 (2003), 357-364.