Geodesic
$Gr$-$(2,n)$-ideals in graded commutative rings
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 129-138.

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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.
DOI : 10.14712/1213-7243.2020.022
Classification : 13A02, 16W50
Keywords: $gr$-$(2, n)$-ideals; $gr$-$2$-absorbing primary ideals; $gr$-prime ideal 
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Al-Zoubi, Khaldoun; Alghueiri, Shatha; Celikel, Ece Y. $Gr$-$(2,n)$-ideals in graded commutative rings. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 129-138. doi : 10.14712/1213-7243.2020.022. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.022/

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