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)Khayyam Journal of Mathematics2423-47886220200701$n$-Absorbing $I$-ideals17417910981410.22034/kjm.2020.109814ENIsmaelAkrayDepartment of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq.MediyaMrakhanDepartment of Mathematics, University of Garmian, Kalar city, Kurdistan
region, Iraq.Journal Article20190410Let $R$ 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 $iin left{1, 2, dots , {n+1} right}$. 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.http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf