TY - JOUR ID - 109814 TI - $n$-Absorbing $I$-ideals JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Akray, Ismael AU - Mrakhan, Mediya AD - Department of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq. AD - Department of Mathematics, University of Garmian, Kalar city, Kurdistan region, Iraq. Y1 - 2020 PY - 2020 VL - 6 IS - 2 SP - 174 EP - 179 KW - $2$-absorbing ideal KW - $n$-absorbing ideal KW - $I$-prime ideal KW - Prime ideal KW - $n$-absorbing $I$-ideal DO - 10.22034/kjm.2020.109814 N2 - 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. UR - https://www.kjm-math.org/article_109814.html L1 - https://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf ER -