SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

On divided and regular divided rings

Chahrazade Bakkari
Pages
1454–1460
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the notion of divided and regular divided rings.
📊
Key Findings & Data:Then we establish the transfer of these notions to trivial ring extension and amalgamated algebras along an ideal.
💡
Conclusion & Impact:The article includes a brief discussion of the scope and precision of our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

🔖

Cite This Article

Bakkari, C. (2022). On divided and regular divided rings. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1454–1460. https://ajindex.com/articles/529709

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (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.