@article {
author = {Akray, Ismael and Mrakhan, Mediya},
title = {$n$-Absorbing $I$-ideals},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {174-179},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109814},
abstract = {Let $R$ be a commutative ring with identity, let $ I $ be a proper ideal of $ R $, and let $ n \ge 1 $ be a positive integer. In this paper, we introduce a class of ideals that is closely related to the class of $I$-prime ideals. A proper ideal $P$ of $R$ is called an {\itshape $n$-absorbing $I$-ideal} if $a_1,\ a_2,\ \dots ,\ a_{n+1} \in R$ with $a_1 a_2 \dots a_{n+1} \in P-IP$, then $a_1 a_2 \dots a_{i-1} a_{i+1} \dots a_{n+1} \in P$ for some $i\in \left\{1,\ 2,\ \dots ,\ {n+1} \right\}$. Among many results, we show that every proper ideal of a ring $R$ is an {\itshape $n$-absorbing $I$-ideal} if and only if every quotient of $ R$ is a product of $(n+1)$-fields.},
keywords = {$2$-absorbing ideal,$n$-absorbing ideal,$I$-prime ideal,Prime ideal,$n$-absorbing $I$-ideal},
url = {http://www.kjm-math.org/article_109814.html},
eprint = {http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf}
}