DM-GAA

Article in press

Authors:

N. Tiprachot

Nuchanat Tiprachot

Department of Mathematics, Faculty of Science, Khon Kaen 40002, Thailand

email: nuchanatt@kkumail.com

0000-0002-0311-2409

B. Pibaljommee

Bundit Pibaljommee

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, Thailand, 40002

email: banpib@kku.ac.th

0000-0001-8263-715X

N. Lekkoksung

Nareupanat Lekkoksung

Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand

email: nareupanat.le@rmuti.ac.th

0000-0002-0026-8387

Title:

On the purities of one-sided ideals in ordered semigroups

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-11-20 , Revised: 2025-02-10 , Accepted: 2025-02-10 , Available online: 2025-10-01 , https://doi.org/10.7151/dmgaa.1493

Abstract:

One of the important principles for characterizing ordered semigroups into classes is the purities of ideals. It was Changphas, and Sanborisoot studied this concept in ordered semigroups. They described left (resp., right) weakly regular ordered semigroups using left (resp., right) pure of two-sided ideals. Our work weakens their study by introducing new kinds of purities for one-sided ideals. We characterize our new version of purities; moreover, a class of ordered semigroups is characterized by this concept.

Keywords:

α-ideal, β-pure, pure ideal, ordered semigroup, regularities

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