Author:
Ulucak Gulsen,Babaei Sakineh,Sevim Esra Sengelen
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, 1-absorbing 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.
Reference7 articles.
1. Idealization of a Module
2. Onn-Absorbing Ideals of Commutative Rings
3. On 1-absorbing primary ideals of commutative rings
4. A. E. Becker, Results on n-absorbing ideals of commutative rings, Ph.D. dissertation, The University of Wisconsin-Milwaukee, 2015.
5. E. A. Behrens and C. Reis, Multiplicative theory of ideals. Academic press, 1971.