Characterization of \((m,n)\)-high-ideals of posemigroups when they are \(0^{\ast}\)-minimal

Authors

  • M. M. Shamivand Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran
  • H. Doostie Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran
  • H. Rasouli Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran

DOI:

https://doi.org/10.26713/cma.v8i1.452

Keywords:

Posemigroup, \((m, n)\)-regular, High-bi-ideal, \(0^{\ast}\)-minimal, n)\)-high-ideal

Abstract

A semigroup \(S\) is called a posemigroup if \(S\) is equipped with a partial ordering relation ``\(\leq\)'' such that \(a \leq b\) in \(S\) implies \(xa \leq xb\) and \(ax \leq bx\), for all \(x\in S\). In this paper, we define an equivalence relation \(\textbf{B}^{\ast}\) 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 \(0^{\ast}\)-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.

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Published

30-06-2017
CITATION

How to Cite

Shamivand, M. M., Doostie, H., & Rasouli, H. (2017). Characterization of \((m,n)\)-high-ideals of posemigroups when they are \(0^{\ast}\)-minimal. Communications in Mathematics and Applications, 8(1), 107–117. https://doi.org/10.26713/cma.v8i1.452

Issue

Vol. 8 No. 1 (2017)

Section

Research Article

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