1. ON n-1-ABSORBING PRIMARY IDEALS.
- Author
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ULUCAK, GULSEN, BABAEI, SAKINEH, and SEVIM, ESRA SENGELEN
- Subjects
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GENERALIZATION , *COMMUTATIVE rings , *COMMUTATIVE algebra , *MATHEMATICAL formulas , *PROOF theory - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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