DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

P. Summaprab

Pisan Summaprab

Department of Mathematics, Rajamangala University of Technology Isan,
Khon Kaen Campus, Khon Kaen 40000, Thailand

email: pisansu9999@gmail.com

Title:

ORDERED SEMIGROUPS IN WHICH PRIME IDEALS ARE MAXIMAL

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Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2023-12-26 , Revised: 2024-06-17 , Accepted: 2024-06-17 , Available online: 2025-03-24 , https://doi.org/10.7151/dmgaa.1474

Abstract:

In this paper, a class of ordered semigroups, namely semipseudo symmetric ordered semigroups, which includes the classes of commutative ordered semigroups, duo ordered semigroups, narmal ordered semigroups and idempotent ordered semigroups is introduced. We obtain a characterization for semipseudo symmetric ordered semigroups with identity in which proper prime ideals are maximal and also characterize semipseudo symmetric ordered semigroups without identity in which proper prime ideals are maximal and the set of all globally idempotent principal ideals forms a chain under the set inclusion.

Keywords:

ordered semigroup, semipseudo symmetric, duo, archimedean, primary ideal, prime ideal, maximal ideal

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