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Dergiler / International Electronic Journal of Algebra / 2024 / Volume: 36 Issue: 36

$\delta (0)$-Ideals of Commutative Rings

Mohamed Chhiti(University S.M. Ben Abdellah)
Bayram Ali Ersoy(YILDIZ TEKNİK ÜNİVERSİTESİ)
Khalid Kaıba(University S.M. Ben Abdellah)
Ünsal Tekir(MARMARA UNIVERSITY)
Sayfa
—
Yayın Tarihi
2024-07-12
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then we investigate the basic properties of $\dt$-ideals and also, we give many examples about $\dt$-ideals.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $R$ be a commutative ring with nonzero identity, let $\I (R)$ be the set of all ideals of $R$ and $\delta : \I (R)\rightarrow\I (R) $ be a function.
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Temel Bulgular & Veri:A proper ideal $I$ of $R$ is called a $\dt$-ideal if whenever $a$, $b$ $\in R$ with $ab\in I$ and $a\notin \delta (0)$, we have $b\in I$.
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Sonuç & Katkı:Then we investigate the basic properties of $\dt$-ideals and also, we give many examples about $\dt$-ideals.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Prime ideal · $\delta$-primary ideal · $n$-ideal

Abstract

Let $R$ be a commutative ring with nonzero identity, let $\I (R)$ be the set of all ideals of $R$ and $\delta : \I (R)\rightarrow\I (R) $ be a function. Then $\delta$ is called an expansion function of ideals of $R$ if whenever $L, I, J$ are ideals of $R$ with $J \subseteq I$, we have $L \subseteq\delta(L)$ and $\delta(J)\subseteq\delta(I)$. In this paper, we present the concept of $\dt$-ideals in commutative rings. A proper ideal $I$ of $R$ is called a $\dt$-ideal if whenever $a$, $b$ $\in R$ with $ab\in I$ and $a\notin \delta (0)$, we have $b\in I$. Our purpose is to extend the concept of $n$-ideals to $\dt$-ideals of commutative rings. Then we investigate the basic properties of $\dt$-ideals and also, we give many examples about $\dt$-ideals.

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Bu Makaleye Atıf Yap

Chhiti, M., Ersoy, B. A., Kaıba, K., Tekir, Ü. (2024). $\delta (0)$-Ideals of Commutative Rings. International Electronic Journal of Algebra, Volume: 36 Issue: 36. https://doi.org/10.24330/ieja.1438744

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Kaynakça (11)

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