MMN-4267
On n-1-absorbing primary ideals
Gulsen Ulucak; Sakineh Babaei; Esra Sengelen Sevim;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.
Vol. 25 (2024), No. 1, pp. 509-522