Authors

Department of Mathematics, Islamic Azad University, Centeral Tehran Branch, Tehran, Iran

Abstract

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.

Keywords

Main Subjects

[1] H. Doostie, L. Pourfaraj, On the minimal ideals of commuting regularrings and semigroups, Internat. J. Appl. Math, 19, NO.2(2006), 201-216.
[2] H. Doostie, L. Pourfaraj, Finite rings and loop rings involving the commutingregular elements, International Mathematical Forum, Vol. 2, NO.52(2007), 2579-2586.
[3] J. M. Howie, Fundamental of Semigroup Theory, Clarendon Prees. Oxford,New York, 1995.
[4] L. Pourfaraj, On the nite groupoid, International Mathematical Forum Vol. 7,2012, no. 23, 1105-1114.
[5] W. B. Vasantha Kandasmy, Groupoids and Smarandachegroupoids, Publishedby the American Reserch Press, 2002, math. GM.