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