arXiv subjects

Suat Koc

Publications and source records attributed to Suat Koc.

2 recordsLinked to original sources

arXiv2021

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

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.

math.AC↗

arXiv2020

Generalization of 2-absorbing quasi primary ideals

In this article, we introduce and study the concept of $ϕ$-2-absorbing quasi primary ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $L(R)$ be the lattice of all ideals of $R$. Suppose that $ϕ:L(R)\rightarrow L(R)\cup\left\{ \emptyset\right\} $ is a function. A proper ideal $I$ of $R$ is called a $ϕ$-2-absorbing quasiprimary ideal of $R$ if $a,b,c\in R$ and whenever $abc\in I-ϕ(I),$ then either $ab\in\sqrt{I}$ or $ac\in\sqrt{I}$ or $bc\in\sqrt{I}$. In addition to giving many properties of $ϕ$-2-absorbing quasi primary ideals, we also use them to characterize von Neumann regular rings.

math.AC↗