RISS 검색 - 국내학술지논문

1
2-absorbing δ-semiprimary Ideals of Commutative Rings

Celikel, Ece Yetkin Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.4
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  ScienceON
  
  KCI
Let R be a commutative ring with nonzero identity, 𝓘(𝓡) the set of all ideals of R and δ : 𝓘(𝓡) → 𝓘(𝓡) an expansion of ideals of R. In this paper, we introduce the concept of 2-absorbing δ-semiprimary ideals in commutative rings which is an extension of 2-absorbing ideals. A proper ideal I of R is called 2-absorbing δ-semiprimary ideal if whenever a, b, c ∈ R and abc ∈ I, then either ab ∈ δ(I) or bc ∈ δ(I) or ac ∈ δ(I). Many properties and characterizations of 2-absorbing δ-semiprimary ideals are obtained. Furthermore, 2-absorbing δ<sub>1</sub>-semiprimary avoidance theorem is proved.
2
On weakly $S$-prime submodules

Hani A. Khashan,Ece Yetkin Celikel 대한수학회 2022 대한수학회보 Vol.59 No.6
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  ScienceON
  
  KCI
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 $S$-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.
3
On weakly $(m,n)$-prime ideals of commutative rings

Hani A. Khashan,Ece Yetkin Celikel 대한수학회 2024 대한수학회보 Vol.61 No.3
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  ScienceON
  
  KCI
Let $R$ be a commutative ring with identity and $m$, $n$ be positive integers. In this paper, we introduce the class of weakly $(m,n)$-prime ideals generalizing $(m,n)$-prime and weakly $(m,n)$-closed ideals. A proper ideal $I$ of $R$ is called weakly $(m,n)$-prime if for $a,b\in R$, $0\neq a^{m}b\in I$ implies either $a^{n}\in I$ or $b\in I$. We justify several properties and characterizations of weakly $(m,n)$-prime ideals with many supporting examples. Furthermore, we investigate weakly $(m,n)$-prime ideals under various contexts of constructions such as direct products, localizations and homomorphic images. Finally, we discuss the behaviour of this class of ideals in idealization and amalgamated rings.
4
On graded $J$-ideals over graded rings

Tamem Al-Shorman,Malik Bataineh,Ece Yetkin Celikel 대한수학회 2023 대한수학회논문집 Vol.38 No.2
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  ScienceON
  
  KCI
The goal of this article is to present the graded $J$-ideals of $G$-graded rings which are extensions of $J$-ideals of commutative rings. A graded ideal $P$ of a $G$-graded ring $R$ is a graded $J$-ideal if whenever $x,y\in h(R)$, if $xy\in P$ and $x\not\in J(R)$, then $y\in P$, where $h(R)$ and $J(R)$ denote the set of all homogeneous elements and the Jacobson radical of $R$, respectively. Several characterizations and properties with supporting examples of the concept of graded $J$-ideals of graded rings are investigated.

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