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arXiv · 2407.16090

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

A. Jamadar
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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.

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A. Jamadar. 2024-07-19. Nil-extensions of simple and right $\pi$-inverse ordered semigroups. https://arxiv.org/abs/2407.16090

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