Article in volume
Authors:
Title:
On right inverse ordered semigroups
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 75-83
Received: 2018-05-27 , Revised: 2020-08-09 , Accepted: 2021-07-31 , Available online: 2022-11-29 , https://doi.org/10.7151/dmgaa.1402
Abstract:
$\newcommand{\rc}{\mathcal{R}}$
A regular ordered semigroup $S$ is called right inverse if every
principal left ideal of $S$ is generated by an $\rc$-unique
positive element of it. We prove that a regular ordered semigroup
is right inverse if and only if any two inverses of an element
$a\in S$ are $\rc$-related. Furthermore the class of right Clifford
ordered semigroups have been characterized by the class of right
inverse ordered semigroups.
Keywords:
ordered regular, ordered inverse, positive element, completely regular, right inverse
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