Weakly prime left ideals in near-subtraction semigroups
Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 325-331 Printed September 1, 2008
P. Dheena and G. Satheesh Kumar Annamalai University
Abstract : In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if $(M,~L)$ is a weak $m^*$-system and if $P$ is a left ideal which is maximal with respect to containing $L$ and not meeting $M,$ then $P$ is weakly prime.
Keywords : subtraction semigroup, near-subtraction semigroup, prime left ideal, weakly prime left ideal