$Gr$-$(2,n)$-ideals in graded commutative rings

@article{Al2020,
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.},
author = {Al-Zoubi, Khaldoun, Alghueiri, Shatha, Celikel, Ece Y.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$gr$-$(2,n)$-ideals; $gr$-$2$-absorbing primary ideals; $gr$-prime ideal},
language = {eng},
number = {2},
pages = {129-138},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$Gr$-$(2,n)$-ideals in graded commutative rings},
url = {http://eudml.org/doc/297189},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Al-Zoubi, Khaldoun
AU - Alghueiri, Shatha
AU - Celikel, Ece Y.
TI - $Gr$-$(2,n)$-ideals in graded commutative rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 2
SP - 129
EP - 138
AB - 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.
LA - eng
KW - $gr$-$(2,n)$-ideals; $gr$-$2$-absorbing primary ideals; $gr$-prime ideal
UR - http://eudml.org/doc/297189
ER -