Open AccessStudying Semigroups Using the Properties of Their Prime m-Ideals
Author(s) -
Mohammad Munir,
Nasreen Kausar,
Bijan Davvaz,
Muhammad Gulistan,
Muhammad Gulzar
Publication year - 2020
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2020.34.109
Subject(s) - mathematics , prime (order theory) , ideal (ethics) , semigroup , prime ideal , boolean prime ideal theorem , pure mathematics , integer (computer science) , minimal ideal , discrete mathematics , maximal ideal , combinatorics , computer science , epistemology , philosophy , programming language
In this article, we present the idea of m-ideals, prime m-ideals and their associated types for a positive integer m in a semigroup. We present different chrarcterizations of semigroups through m-ideals. We demonstrate that the ordinary ideals, and their relevent types differ from the m-ideals and their assocated types by presenting concrete examples on the maximal, irreducible and strongly irreducible m-ideals. We conclude from the study that the introduction of the m-ideal will explore new fields of studies in semigroups and their applications.