KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
—
Yayın Tarihi
2021-04-11
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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.