Algebraic and logical methods in computer science and artificial intelligence

Studying semigroups using the properties of their prime $m$-ideals

M. Munir^a, N. Kausar^b, B. Davvaz^c, M. Gulistan^d, M. Gulzar<sup>e

a</sup> Government Postgraduate College, Abbottabad, Pakistan
^b Agriculture University, Faisalabad, Pakistan
^c Yazd University, Yazd, Iran
^d Hazara University, Mansehra, Pakistan
^e Government College University Faisalabad, Pakistan

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.

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

Received: 08.06.2020

Language: English

DOI: 10.26516/1997-7670.2020.34.109

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