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Ece Yetkin Celikel

Publications and source records attributed to Ece Yetkin Celikel.

18 recordsLinked to original sources
arXiv2026

Quasi sdf-absorbing ideals in commutative rings

This paper introduces and studies quasi sdf-absorbing ideals as a generalization of sdf-absorbing ideals. We investigate the stability of this property under various constructions, including localization, surjective images, Nagata idealizations, and amalgamations. We establish conditions under which the radical of such ideals is prime and discuss a specific class of rings where quasi sdf-absorption implies the sdf-absorbing primary property. The study concludes with a classification of these ideals in Z and examples distinguishing them from related ideal classes.

math.AC↗
arXiv2026

Generalized square-difference factor absorbing submodules of modules over commutative rings

In this paper, we introduce and study the class of generalized square-difference factor absorbing (gsdf-absorbing) submodules of modules over commutative rings. We provide various characterizations and properties of gsdf-absorbing submodules and examine the behavior of this class of submodules in some module extensions, including localization, homomorphic images, direct products, idealization, and amalgamation. We also characterize all gsdf-absorbing submodules of the Z-module Z. Several examples are provided to illustrate the results and to distinguish this class from related notions.

math.AC↗
arXiv2025

Semi n-submodules of modules over commutative rings

Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is called a semi $n$-submodule if whenever $r\in R$, $m\in M$ with $r^{2}m\in N$, $r\notin\sqrt{0}$ and $Ann_{R}(m)=0$, then $rm\in N$. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi $n$-submodules of amalgamated modules are investigated.

math.AC↗
arXiv2022

Semi r-ideals of commutative rings

For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if whenever $a^{2}\in I$ and $Ann_{R}(a)=0$, then $a\in I$. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi $r$-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi $r$-ideals of rings to semi $r$-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the $D$-annihilator condition and justify when they are semi $r$-submodules.

math.AC↗
arXiv2022

On Weakly S-primary Submodules

Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ to be weakly $S$-primary if there exists $s\in S$ such that whenever $a\in R$ and $m\in M$ with $0\neq am\in N$, then either $sa\in\sqrt{(N:_{R}M)}$ or $sm\in N$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Moreover, the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations is investigated. Finally, we determine some conditions under which two kinds of submodules of the amalgamation module along an ideal are weakly $S$-primary.

math.AC↗
arXiv2022

S-1-absorbing primary submodules

In this work, we introduce the notion of $S$-1-absorbing primary submodule as an extension of 1-absorbing primary submodule. Let $S$ be a multiplicatively closed subset of a ring $R$ and $M$ be an $R$-module. A submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be $S$-1-absorbing primary if whenever $abm\in N$ for some non-unit $a,b\in R$ and $m\in M$, then either $sab\in(N:_{R}M)$ or $sm\in M$-$rad(N)$. We examine several properties of this concept and provide some characterizations. In addition, $S$-1-absorbing primary avoidance theorem and $S $-1-absorbing primary property for idealization and amalgamation are presented.

math.AC↗
arXiv2021

On weakly S-prime submodules

Let $R$ be a commutative ring with a non-zero identity, $S$ be a multiplicatively closed subset of $R$ and $M$ be a unital $R$-module. In this paper, we define a submodule $N$ of $M$ with $(N:_{R}M)\cap S=ϕ$ to be weakly $S$-prime if there exists $s\in S$ such that whenever $a\in R$ and $m\in M$ with $0\neq am\in N$, then either $sa\in(N:_{R}M)$ or $sm\in N$. Many properties, examples and characterizations of weakly $S$-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly $S$-prime.

math.AC↗
arXiv2021

S-n-ideals of Commutative Rings

Let $R$ be a commutative ring with identity and $S$ a multiplicatively closed subset of $R$. This paper aims to introduce the concept of $S$-$n$-ideals as a generalization of $n$-ideals. An ideal $I$ of $R$ disjoint with $S$ is called an $S$-$n$-ideal if there exists $s\in S$ such that whenever $ab\in I$ for $a,b\in R$, then $sa\in\sqrt{0}$ or $sb\in I$. The relationship among $S$% -$n$-ideals, $n$-ideals, $S$-prime and $S$-primary ideals are clarified. Several properties, characterizations and examples are presented such as investigating $S$-$n$-ideals under various contexts of constructions including direct products, localizations and homomorphic images. Furthermore, for $m\in% %TCIMACRO{\U{2115} }% %BeginExpansion \mathbb{N} %EndExpansion $ and some particular $S$, all $S$-$n$-ideals of the ring $% %TCIMACRO{\U{2124} }% %BeginExpansion \mathbb{Z} %EndExpansion _{m}$ are completely determined. The last section is devoted for studying the $S$-$n$-ideals of the idealization ring and amalgamated algebra.

math.AC↗
arXiv2021

Weakly J-submodules of Modules over Commutative Rings

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. By $J(R),$ we denote the Jacobson radical of $R$. The purpose of this paper is to introduce the concept of weakly $J$-submodules generalizing $J$-submodules. We call a proper submodule $N$ of $M$ a weakly $J$-submodule if whenever $0\neq rm\in N$ for $r\in R$ and $m\in M$, then $r\in(J(R)M:M)$ or $m\in N.$ Various properties and characterizations of weakly $J$-submodules are investigated especially in the case of multiplication modules.

math.AC↗
arXiv2021

$δ$-$n$-ideals of commutative rings

Let $R$ be a commutative ring with nonzero identity, and $δ:\mathcal{I(R)}\rightarrow\mathcal{I(R)}$ be an ideal expansion where $\mathcal{I(R)}$ the set of all ideals of $R$. In this paper, we introduce the concept of $δ$-$n$-ideals which is an extension of $n$-ideals in commutative rings. We call a proper ideal $I$ of $R$ a $δ$-$n$-ideal if whenever $a,b\in R$ with$\ ab\in I$ and $a\notin\sqrt{0}$, then $b\in δ(I)$. For example, $δ_{1}$ is defined by $δ_{1}(I)=\sqrt{I}.$ A number of results and characterizations related to $δ$-$n$-ideals are given. Furthermore, we present some results related to quasi $n$-ideals which is for the particular case $δ=δ_{1}.$

math.AC↗
arXiv2021

1-absorbing primary submodules

Let $R$ be a commutative ring with non-zero identity and $M$ be a unitary $R$-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule $N$ of $M$ is said to be a 1-absorbing primary submodule if whenever non-unit elements $a,b\in R$ and $m\in M$ with $abm\in N$, then either $ab\in(N:_{R}M)$ or $m\in M-rad(N).$ Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved.

math.AC↗
arXiv2021

Weakly J-ideals of Commutative Rings

Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly $J$-ideals as a new generalization of $J$-ideals. We call a proper ideal $I$ of a ring $R$ a weakly $J$-ideal if whenever $a,b\in R$ with $0\neq ab\in I$ and $a\notin J(R)$, then $a\in I$. Many of the basic properties and characterizations of this concept are studied. We investigate weakly $J$-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly $J$-ideals are discussed. Finally, the third section is devoted to the characterizations of these constructions in an amagamated ring along an ideal.

math.AC↗
arXiv2021

Quasi J-ideals of Commutative Rings

Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of quasi $J$-ideal which is a generalization of $J$-ideal. A proper ideal of $R$ is called a quasi $J$-ideal if its radical is a $J$-ideal. Many characterizations of quasi $J$-ideals in some special rings are obtained. We characterize rings in which every proper ideal is quasi $J$-ideal. Further, as a generalization of presimplifiable rings, we define the notion of quasi presimplifiable rings. We call a ring $R$ a quasi presimplifiable ring if whenever $a,b\in R$ and $a=ab$, then either $a$ is a nilpotent or $b$ is a unit. It is shown that a proper ideal $I$ that is contained in the Jacobson radical is a quasi $J$-ideal (resp. $J$-ideal) if and only if $R/I$ is a quasi presimplifiable (resp. presimplifiable) ring.

math.AC↗
arXiv2021

Quasi J-submodules

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a quasi $J$-submodule if whenever $r\in R$ and $m\in M$ such that $rm\in N$ and $r\notin(J(R)M:M)$, then $m\in M$-$rad(N)$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) $J$-submodules. Finally, for a submodule $N$ of $M$ and an ideal $I$ of $R$, we characterize the quasi $J$-ideals of the idealization ring $R(+)M$.

math.AC↗
arXiv2020

On Weakly 1-absorbing Primary Ideals of Commutative Rings

Let R be a commutative ring with $1\neq0$. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal. A proper ideal $I$ of $R$ is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c\in R$ and $0\neq abc\in I,$ then $ab\in I$ or $c\in\sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. Furthermore, we give the correct version of a result on 1-absorbing ideals of commutative rings.

math.RA↗
arXiv2016

On (k,n)-closed submodules

Let R be a commutative ring with unity and M be an R- module In this paper we introduce semi n- absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties.

math.AC↗
arXiv2016

On quasi n-absorbing elements of multiplicative lattices

In this study, we introduce the concept of quasi n-absorbing elements of multiplicative lattices. A proper element q is said to be a quasi n-absorbing element of L if whenever $a^nb\le q$ implies that either $a^n\le q$ or $a^{n-1}b\le q$. We investigate properties of this new type of elements and obtain some relations among prime, 2-absorbing, n-absorbing elements in multiplicative lattices.

math.RA↗