Geodesic
On right inverse ordered semigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 75-83

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A regular ordered semigroup S is called right inverse if every principal left ideal of S is generated by an ℛ-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∈ S are ℛ-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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Jamadar, Amlan; Hansda, Kalyan. On right inverse ordered semigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 75-83. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a6/