Nil-extensions of simple and right $\pi$-inverse ordered semigroups

A. Jamadar

Nil-extensions of simple and right $\pi$-inverse ordered semigroups

Group Theory 2024-07-24 v1

Authors: A. Jamadar

Abstract

An ordered semigroup $S$ is right $\pi$ -inverse if it is $\pi$ -inverse but not conversely. So the question arises under what condition the converse holds. In this paper we study nil-extensions of simple and right $\pi$ -inverse ordered semigroups and prove that $S$ is right $\pi$ -inverse if and only if $S$ is $\pi$ -inverse in a $t$ -Archimedean ordered semigroup. Moreover, we characterize complete semilattice of nil-extensions of simple and right $\pi$ -inverse ordered semigroups.

Keywords

ordered semigroup right $\pi$-inverse nil-extensions simple semigroup t-Archimedean

Cite

@article{arxiv.2407.16090,
  title  = {Nil-extensions of simple and right $\pi$-inverse ordered semigroups},
  author = {A. Jamadar},
  journal= {arXiv preprint arXiv:2407.16090},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with 2407.14569; text overlap with arXiv:1701.07189, arXiv:1701.07185 by other authors

Nil-extensions of simple and right $\pi$-inverse ordered semigroups

Abstract

Keywords

Cite

Comments

Related papers