Khaldoun Al-Zoubi, Shatha Alghueiri, Ece Y. Celikel
$Gr$-$(2,n)$-ideals in graded commutative rings

Comment.Math.Univ.Carolin. 61,2 (2020) 129-138.

Abstract:Let $G$ be a group with identity $e$ and let $R$ be a $G$-graded ring. In this paper, we introduce and study the concept of graded $(2,n)$-ideals of $R$. A proper graded ideal $I$ of $R$ is called a graded $(2,n)$-ideal of $R$ if whenever $rst\in I$ where $r,s,t\in h(R)$, then either $rt\in I$ or $rs\in Gr(0)$ or $st\in Gr(0)$. We introduce several results concerning $gr$-$(2,n)$-ideals. For example, we give a characterization of graded $(2,n)$-ideals and their homogeneous components. Also, the relations between graded $(2,n)$-ideals and others that already exist, namely, the graded prime ideals, the graded 2-absorbing primary ideals, and the graded $n$-ideals are studied.

Keywords: $gr$-$(2,n)$-ideals; $gr$-$2$-absorbing primary ideals; $gr$-prime ideal

DOI: DOI 10.14712/1213-7243.2020.022
AMS Subject Classification: 13A02 16W50