IJPAM: Volume 61, No. 1 (2010)

PRE-INVERSE SUBGROUPS OF ORTHODOX SEMIGROUPS

S. Hussain$^1$, T. Anwar$^2$
$^{1,2}$Department of Mathematics
Quaid-i-Azam University
Islamabad, 45320, PAKISTAN
$^1$e-mail: fbsaso@gmail.com
$^2$e-mail: tariqanwar79@yahoo.co.in


Abstract.In this paper we consider a regular semigroup $S$ and a subsemigroup $T$ having the property that $T\cap A(a)\neq \emptyset $ for every $a$ belongs to $S\setminus T,$ and show that $T$ is a maximal subgroup $H_{z}$ for some idempotent $z.$ When $S$ is orthodox, $z$ is medial and $zSz$ is uniquely unit orthodox. When $S$ is orthodox and $z$ is a middle unit, we obtain a structure theorem for uniquely unit orthodox semigroup.

Received: March 20, 2010

AMS Subject Classification: 47D60

Key Words and Phrases: ortodox, pre-inverse, medial, middle unit

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 1