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arXiv · 2107.04659

On Graded $ϕ$-$1$-absorbing prime ideals

Mashhoor Refai·Rashid Abu-Dawwas·Unsal Tekir·Suat Koc·Roa'a Awawdeh·Eda Yildiz
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Abstract

Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all graded ideals of $R$. Suppose that $ϕ:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article, we introduce and study the concept of graded $ϕ$-$1$-absorbing prime ideals. A proper graded ideal $I$ of $R$ is called a graded $ϕ$% -$1$-absorbing prime ideal of $R$ if whenever $a,b,c$ are homogeneous nonunit elements of $R$ such that $abc\in I-ϕ(I)$, then $ab\in I$ or $c\in I$. Several properties of graded $ϕ$-$1$-absorbing prime ideals have been examined.

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Mashhoor Refai, Rashid Abu-Dawwas, Unsal Tekir, Suat Koc, Roa'a Awawdeh, Eda Yildiz. 2021-08-04. On Graded $ϕ$-$1$-absorbing prime ideals. https://arxiv.org/abs/2107.04659

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