On strongly regular near-subtraction semigroups
Commun. Korean Math. Soc. 2007 Vol. 22, No. 3, 323-330
Printed September 1, 2007
P. Dheena, G. Satheesh Kumar
Annamalai University, Annamalai University
Abstract : In this paper we introduce the notion of strongly regular near-subtraction semigroups (right). We have shown that a near-subtraction semigroup X is strongly regular if and only if it is regular and without non zero nilpotent elements. We have also shown that in a strongly regular near-subtraction semigroup $X,$ the following holds: (i) $Xa$ is an ideal for every $a \in X$ (ii) If $P$ is a prime ideal of $X,$ then there exists no proper $k$-ideal $M$ such that $P \subset M$ (iii) Every ideal $I$ of $X$ fulfills $I=I^2.$
Keywords : subtraction semigroup, near-subtraction semigroup, regular, strongly regular
MSC numbers : 06F35, 16Y30
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