ON n-1-ABSORBING PRIMARY IDEALS

Abstract

The paper aims to present a new primary ideal in a commutative ring R with nonzero identity element. We introduce the new primary ideal as an n-1-absorbing primary ideal that is a generalization of both primary and 1-absorbing primary ideals. We propose to achieve two goals with this paper. Firstly, we study and characterize some essential properties of an n-1-absorbing primary ideals and figure out the relations between the other types of ideals such as prime, 1absorbing primary and irreducible ideals. Then, we classify some special rings that admit an n-1-absorbing primary ideal. We provide the results by introducing some examples.