KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 5

On divided and regular divided rings

Chahrazade Bakkari0000-0002-6387-7972
Sayfa
—
Yayın Tarihi
2019-10-08
DOI
—
🏛️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)

The article includes a brief discussion of the scope and precision of our results.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study the notion of divided and regular divided rings.
📊
Temel Bulgular & Veri:Then we establish the transfer of these notions to trivial ring extension and amalgamated algebras along an ideal.
💡
Sonuç & Katkı:The article includes a brief discussion of the scope and precision of our results.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:divided ring · regular divided ring · trivial ring extension

Abstract

In this paper, we study the notion of divided and regular divided rings. Then we establish the transfer of these notions to trivial ring extension and amalgamated algebras along an ideal. These results provide examples of non-divided regular divided rings. The article includes a brief discussion of the scope and precision of our results.

🔖

Bu Makaleye Atıf Yap

Bakkari, C. (2019). On divided and regular divided rings. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 5. https://ajindex.com/articles/1402744

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. K. Alaoui Ismaili and N. Mahdou, n-coherence property in amalgamated algebra along an ideal, Acta Math. Univ. Comenian. (N.S.), 86 (1), 59–72, 2017.
  2. A. Badawi, On divided commutative rings, Comm. Algebra, 27, 1465-1474, 1999.
  3. A. Badawi and D.E. Dobbs, On locally divided rings and going-down rings, Comm. Algebra, 29, 2805-2825, 2001.
  4. C. Bakkari, S. Kabbaj and N. Mahdou, Trivial extension defined by Prüfer condition, J. Pure Appl. Algebra, 214, 53–60, 2010.
  5. M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat. 45 (2), 241–252, 2007.
  6. M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. 6 (3), 443–459, 2007.
  7. M. D’Anna, C.A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, in: Commutative algebra and its applications, Walter de Gruyter, Berlin, 241–252, 2009.
  8. M. D’Anna, C.A Finocchiaro and M. Fontana, Properties of prime ideals in an amalgamated algebra along an ideal, J. Pure Appl. Algebra, 214, 1633–1641, 2010.
  9. M. D’Anna, C.A Finocchiaro and M. Fontana, Algebraic and topological properties of an amalgamated algebra along an ideal, Comm. Algebra, 44, 1836-1851, 2016.
  10. D.E. Dobbs, Divided rings and going-down, Pac. J. Math. 67 (2), 353-363, 1976.
  11. D.E. Dobbs and J. Shapiro, A generalization of divided domains and its connection to weak Baer going-down rings, Comm. Algebra, 37, 3553-3572, 2009.
  12. S. Glaz, Commutative Coherent Rings, Springer-Verlag, Lecture Notes in Mathe- matics, 1371, 1989.
  13. J.A. Huckaba, Commutative Rings with Zero Divizors, Marcel Dekker, New York Basel, 1988.
  14. S. Kabbaj and N. Mahdou, Trivial Extensions Defined by coherent-like condition, Comm. Algebra, 32 (10), 3937–3953, 2004.
  15. N. Mahdou and M.A. Moutui, fqp-property in amalgamated algebras along an ideal, Asian-Eur. J. Math. 8 (3), 2015.
  16. N. Mahdou, M. Chhiti and M. Tamekkante Clean property in Amalgamated algebras along an ideal, Hacet. J. Math. Stat. 44 (1), 41–49, 2015.
  17. N. Mahdou, A. Mimouni and M.A. Moutui, On almost valuation and almost Bézout rings, Comm. Algebra, 43, 297–308, 2015.
  18. H.R. Maimani and S. Yassemi, Zero-divisor graphs of amalgamated duplication of a ring along an ideal, J. Pure Appl. Algebra, 212 (1), 168–174, 2008.
  19. G. Picavet, Ideals and overring of divided domains, Int. Electron. J. Algebra, 8, 80–113, 2009.