KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

On LPI rings

Rachida El Khalfaoui(University S.M. Ben Abdellah)0000-0003-0830-0481
Najib Mahdou(University S.M. Ben Abdellah)0000-0001-6353-1114
Abdeslam Mimouni(King Fahd University of Petroleum & Minerals)0000-0001-5865-2683
Sayfa
—
Yayın Tarihi
2020-04-02
🏛️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)

Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we extend the $LPI$ property (that is, every locally principal ideal in an integral domain is invertible) to rings with zero-divisors and we study the class of commutative rings in which every regular locally principal ideal is invertible called $LPI$ rings.
📊
Temel Bulgular & Veri:We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, amalgamation of rings and trivial ring extensions.
💡
Sonuç & Katkı:Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Locally principal ideals · regular ideals · trivial extension

Abstract

In this paper, we extend the $LPI$ property (that is, every locally principal ideal in an integral domain is invertible) to rings with zero-divisors and we study the class of commutative rings in which every regular locally principal ideal is invertible called $LPI$ rings. We investigate the stability of this property under homomorphic image, and its transfer to various contexts of constructions such as direct products, amalgamation of rings and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

🔖

Bu Makaleye Atıf Yap

Khalfaoui, R. E., Mahdou, N., Mimouni, A. (2020). On LPI rings. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.456426

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (22)

  1. M.M. Ali, Idealization and Theorems of D.D. Anderson, Comm. Algebra 34, 4479- 4501, 2006.
  2. M.M. Ali, Idealization and Theorems of D.D. Anderson II, Comm. Algebra 35, 2767- 2792, 2007.
  3. D.D. Anderson and A. Mimouni, LPI domains and Pullbacks, Comm. Algebra 42, 2759-2768, 2014.
  4. D.D. Anderson and M. Roitman, A characterization of cancellation ideals, Proc. Amer. Math. Soc. 125, 2853-2854, 1997.
  5. D.D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra 1 (1), 3-56, 2009.
  6. D.D. Anderson and M. Zafrullah, Integral domains in which nonzero locally principal ideals are invertible, Comm. Algebra 39, 933-941, 2011.
  7. C. Bakkari, S. Kabbaj and N. Mahdou, Trivial extension definided by Prûfer conditions, J. Pure App. Algebra 214, 53-60, 2014.
  8. S. Bazzoni, Class semigroups of Prüfer domains, J. Algebra 184, 613-631, 1996.
  9. M. D’Anna, C.A. Finocchiaro and M. Fontana, Amalgamated algebra along an ideal, Commmutative Algebra and Applications, Walter De Gruyter, 155-172, 2009.
  10. M. D’Anna, C.A. Finocchiaro and M. Fontana, Properties of chains of prime ideals in amalgamated algebras along an ideal, J. Pure Appl. Algebra 214, 1633-1641, 2010.
  11. M. D’Anna, C.A. Finocchiaro and M. Fontana, New algebraic properties of an amalgamated algebra along an ideal, Comm. Algebra 44, 1836-1851, 2016.
  12. M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. 6, 443-459, 2007.
  13. S. Glaz, Commutative coherent rings, Springer-Verlag, Lecture Notes in Mathematics, 13-71, 1989.
  14. S. Glaz and W. Vasconcelos, Flat ideals II, Manuscripta Math. 22 (4), 325-341, 1977.
  15. F. Halter-Koch, Clifford semigroups of ideals in monoids and domains, Forum Math. 21, 1001-1020, 2009.
  16. W.C. Holland, J. Martinez, W.Wm. McGovern and M. Tesemma, Bazzoni’s Conjecture, J. Algebra 320, 1764-1768, 2008.
  17. K. Hu, F.G. Wang and H. Chen, A note on LPI domains, Bull. Korean Math. Soc. 50 (3), 719-725, 2013.
  18. J.A. Huckaba, Commutative rings with zero divisors, Marcel Dekker, New York- Basel,1988.
  19. K. Louartiti and N. Mahdou, Transfer of multiplication-like conditions in amalgamated algebra along an ideal, Afr. Diaspora J. Math. 14 (1), 119-125, 2012.
  20. G. Picozza and F. Tartarone, Flat ideals and stability in integral domains, J. Algebra 324, 1790-1802, 2010.
  21. J. Sally and W. Vasconcelos, Flat ideals I, Comm. Algebra 3 531-543, 1975.
  22. S. Xing and F.G. Wang, Two questions on domains in which locally principal ideals are invertible. J. Algebra Appl. 16 (6), 1750112, 8 pp, 2017.