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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2020. Vol. 34

Studying Semigroups Using the Properties of Their Prime m-Ideals

Author(s)
M. Munir, N. Kausar, B. Davvaz, M. Gulistan, M. Gulzar
Abstract

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.

About the Authors

M. Munir, Dr., Assoc. Prof. of Mathematics, Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan, email: dr.mohammadmunri@gmail.com

N. Kausar, Dr., Assistant Prof. of Mathematics, Department of Mathematics and Statistics, Agriculture University, Faisalabad, Pakistan, email: kausar.nasreen57@gmail.com

B. Davvaz, Dr., Prof. of Mathematics, Department of Mathematics, Yazd University, Yazd, Iran, email: davvaz@yazd.ac.ir

M. Gulistan, Dr., Assistant Prof., Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan, email: gulistanmath@hu.edu.pk

M. Gulzar, Department of Mathematics, Government College University Faisalabad, Pakistan, email: 98kohly@gmail.com

For citation

Munir M., Kausar N., Davvaz B., Gulistan M., Gulzar M. Studying Semigroups Using the Properties of Their Prime m-Ideals. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 34, pp. 109-125. https://doi.org/10.26516/1997-7670.2020.34.109

Keywords

completely prime m-ideals, strongly prime m-ideals, maximal m-ideals, irreducible m-ideals, strongly Irreducible m-ideals

UDC
512.53
MSC
20M12, 20M99
DOI
https://doi.org/10.26516/1997-7670.2020.34.109
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