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arXiv · 1706.08214

On inverse and right inverse ordered semigroups

A. Jamadar·K. Hansda
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Abstract

A regular ordered semigroup $S$ is called right inverse if every principal left ideal of $S$ is generated by an $\mathcal{R}$-unique ordered idempotent. Here we explore the theory of right inverse ordered semigroups. We show that a regular ordered semigroup is right inverse if and only if any two right inverses of an element $a\in S$ are $\mathcal{R}$-related. Furthermore, different characterizations of right Clifford, right group-like, group like ordered semigroups are done by right inverse ordered semigroups. Thus a foundation of right inverse semigroups has been developed.

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A. Jamadar, K. Hansda. 2017-06-26. On inverse and right inverse ordered semigroups. https://arxiv.org/abs/1706.08214

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