Characterization of \((m,n)\)-high-ideals of posemigroups when they are \(0^*\)-minimal - Shamivand, M. M.; Doostie, H.; Rasouli, H. (Communications in Mathematics and Applications, 2017)
A semigroup \(S\) is called a posemigroup if \(S\) is equipped with a partial ordering relation ``\(≤\)’’ such that \(a ≤ b\) in \(S\) implies \(xa ≤ xb\) and \(ax ≤ bx\), for all \(xS\). In this paper, we define an equivalence relation \(B^*\) on a posemigroup \(S\) and introduce the concept of \((m,n)\)-high-ideals by generalizing the concept of \((m,n)\)-ideals in a posemigroup, for two non-negative integers \(m\) and \(n\). As a result of this definition we get a relationship between \(0^*\)-minimal \((m,n)\)-high-ideals and \((m,n)\)-regular posemigroups. A necessary and sufficient condition for a posemigroup \(S\) to be an \((m,n)\)-regular posemigroup is given as well.