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Kyungpook Mathematical Journal 2022; 62(3): 425-436

Published online September 30, 2022

Copyright © Kyungpook Mathematical Journal.

On 2-absorbing Primary Ideals of Commutative Semigroups

Manasi Mandal∗ and Biswaranjan Khanra

Department of Mathematics, Jadavpur University, Kolkata-700032, India
e-mail : manasi_ju@yahoo.in and biswaranjanmath91@gmail.com

Received: January 5, 2021; Revised: April 24, 2022; Accepted: May 3, 2022

Abstract

In this paper we introduce the notion of 2-absorbing primary ideals of a commutative semigroup. We establish the relations between 2-absorbing primary ideals and prime, maximal, semiprimary and 2-absorbing ideals. We obtain various characterization theorems for commutative semigroups in which 2-absorbing primary ideals are prime, maximal, semiprimary and 2-absorbing ideals. We also study some other important properties of 2-absorbing primary ideals of a commutative semigroup.

Keywords: Commutative semigroup, Prime ideal, Maximal ideal, Semiprime ideal, Semiprimary ideal, 2-absorbing ideal