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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

The singular ideal and the socle of incidence rings

Müge Kanuni Er(DUZCE UNIVERSITY)0000-0001-7436-039X
Özkay Özkan(GEBZE TECHNICAL UNIVERSITY)0000-0001-6755-1497
Pages
—
Publication Date
2021-04-11
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⚡ TL;DR(Too Long; Didn't Read)

Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.
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Key Findings & Data:Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.
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Conclusion & Impact:Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:incidence algebras · socle · singular ideal

Abstract

Let $R$ be a ring with identity and $I(X,R)$ be the incidence ring of a locally finite partially ordered set $X$ over $R.$ In this paper, we compute the socle and the singular ideal of the incidence ring for some $X$ in terms of the socle of $R$ and the singular ideal of $R$, respectively.

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Cite This Article

Er, M. K., Özkan, Ö. (2021). The singular ideal and the socle of incidence rings. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.684042

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References (6)

  1. F. Al-Thukair, S. Singh and I. Zaguia, Maximal ring of quotients of an incidence algebra, Arch. Math. 80, 358–362, 2003.
  2. S. Esin, M. Kanuni and A. Koç, Characterization of some ring properties in incidence algebras, Comm. Algebra, 39 (10), 3836–3848, 2011.
  3. M. Kanuni, Dense ideals and maximal quotient rings of incidence algebras, Comm. Algebra, 31 (11), 5287–5304, 2003.
  4. T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics 189, New York-Berlin, Springer-Verlag, 1999.
  5. E. Spiegel, Essential ideals of incidence algebras, J. Austral. Math. Soc. (Series A), 68, 252–260, 2000.
  6. E. Spiegel and C.J. O’Donnell, Incidence Algebras, Monographs and Textbooks in Pure Appl. Math. 206, New York, Marcel Dekker, 1997.