Ordered constraint semigroups‎: ‎a novel class of algebraic systems

Volume 37, Issue 2, pp 201--213 https://dx.doi.org/10.22436/jmcs.037.02.05

Publication Date: September 25, 2024 Submission Date: September 04, 2023 Revision Date: August 01, 2024 Accteptance Date: August 19, 2024

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Authors

P‎. ‎ Palakawong na Ayutthaya - Department of Mathematics‎, ‎Faculty of Science, ‎Khon Kaen University, ‎Khon Kaen 40002, ‎Thailand. ‎N‎. ‎ Lekkoksung - Division of Mathematics‎, ‎Faculty of Engineering, ‎Rajamangala University of Technology Isan, ‎‎Khon Kaen Campus‎, Khon Kaen 40000, ‎Thailand.

Abstract

‎The distinguishing factor between semigroups and ordered semigroups lies in compatibility‎. ‎Compatibility is a specific form of polymorphisms‎, ‎an essential tool in clone theory‎. ‎In this paper‎, ‎we apply a generalized version of polymorphisms‎, ‎known as constraint‎, ‎to define a novel algebraic structure called ordered constraint semigroups‎. ‎It turns out that ordered constraint semigroups are generalizations of semigroups‎. ‎We define various ideals in ordered constraint semigroups and examine their fundamental properties‎. ‎Specifically‎, ‎we investigate their generated forms and explore the relationships among these ideals‎. ‎Moreover‎, ‎we focus on the intersection property of quasi-ideals in ordered constraint semigroups‎.

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Keywords

• Ordered semigroups
• constraints
• ordered constraint semigroups
• ideals

MSC

•  06F05
•  08A05
•  20M12

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