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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

Zero intersection graph of annihilator ideals of modules

Seçil Çeken(TRAKYA UNIVERSITY)0000-0002-7578-9320
Osama A. Naji(SAKARYA UNIVERSITY)0000-0002-6498-7620
Ünsal Tekir(MARMARA UNIVERSITY)0000-0003-0739-1449
Suat Koç(ISTANBUL MEDENIYET UNIVERSITY)0000-0003-1622-786X
Sayfa
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Yayın Tarihi
2025-12-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Furthermore, we characterize certain classes of modules and rings such as torsion-free modules, torsion modules, semisimple modules, quasi-regular rings, and modules satisfying Property $T$ in terms of their graphical properties.

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Amaç & Hipotez:This paper aims to associate a new graph to nonzero unital modules over commutative rings.
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Temel Bulgular & Veri:The zero intersection graph of annihilator ideals of $R$-module $M$, denoted by $\mathfrak{C}_{R}(M)$, is a simple (undirected) graph whose vertex set $M^{\star}=M-\{0\},\ $and two distinct vertices $m$ and $m^{\prime}$ are adjacent if $ann_{R}(m)\cap ann_{R}(m^{\prime})=(0).$\ We investigate the conditions under which $\mathfrak{C}_{R}(M)$ is a star graph, bipartite graph, complete graph, edgeless graph.
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Sonuç & Katkı:Furthermore, we characterize certain classes of modules and rings such as torsion-free modules, torsion modules, semisimple modules, quasi-regular rings, and modules satisfying Property $T$ in terms of their graphical properties.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:property A · property T · torsion-free module

Abstract

This paper aims to associate a new graph to nonzero unital modules over commutative rings. Let $R$ be a commutative ring having a nonzero identity and $M$ be a nonzero unital $R$-module. The zero intersection graph of annihilator ideals of $R$-module $M$, denoted by $\mathfrak{C}_{R}(M)$, is a simple (undirected) graph whose vertex set $M^{\star}=M-\{0\},\ $and two distinct vertices $m$ and $m^{\prime}$ are adjacent if $ann_{R}(m)\cap ann_{R}(m^{\prime})=(0).$\ We investigate the conditions under which $\mathfrak{C}_{R}(M)$ is a star graph, bipartite graph, complete graph, edgeless graph. Furthermore, we characterize certain classes of modules and rings such as torsion-free modules, torsion modules, semisimple modules, quasi-regular rings, and modules satisfying Property $T$ in terms of their graphical properties.

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Bu Makaleye Atıf Yap

Çeken, S., Naji, O. A., Tekir, Ü., Koç, S. (2025). Zero intersection graph of annihilator ideals of modules. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1485903

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