SavedAdd your journal

Journals / International Electronic Journal of Algebra / 2014 / Cilt: 15 - Sayı: 15

ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS

Alejandro Alvarado-García
César Cejudo-Castilla
Hugo Alberto Rincón-Mejía
Ivan Fernando Vilchis-Montalvo
Pages
1–12
Publication Date
2014-06-01
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)

We obtain some characterizations of artinian principal ideal rings using properties of big lattices of module classes.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work we consider some classes of modules closed under certain closure properties such as being closed under taking submodules, quotients, injective hulls and direct sums.
📊
Key Findings & Data:In this work we consider some classes of modules closed under certain closure properties such as being closed under taking submodules, quotients, injective hulls and direct sums.
💡
Conclusion & Impact:We obtain some characterizations of artinian principal ideal rings using properties of big lattices of module classes.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Artinian principal ideal rings · big lattices of module classes · QF-rings

Abstract

In this work we consider some classes of modules closed under certain closure properties such as being closed under taking submodules, quotients, injective hulls and direct sums. We obtain some characterizations of artinian principal ideal rings using properties of big lattices of module classes.

🔖

Cite This Article

Alvarado-García, A., Cejudo-Castilla, C., Rincón-Mejía, H. A., Vilchis-Montalvo, I. F. (2014). ON CLASSES OF MODULES CLOSED UNDER INJECTIVE HULLS AND ARTINIAN PRINCIPAL IDEAL RINGS. International Electronic Journal of Algebra, Cilt: 15 - Sayı: 15, 1–12. https://ajindex.com/articles/832418

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. A. Alvarado, H. Rinc´on and J. R´ıos, On some lattices of module classes, J. Algebra Appl., 5(1) (2006), 105-117.
  2. F. Anderson and K. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1992.
  3. A. Boyle, When projective covers and injective hulls are isomorphic, Bull. Aus- tral. Math. Soc., 8 (1973), 471-476.
  4. R. Bronowitz and M. L. Teply, Torsion theories of simple type, J. Pure Appl. Algebra, 3 (1973), 329-336.
  5. A. El Mejdani, H. Essannouni and A. Kaidi, Rings with nice Artinian Modules, Int. J. Algebra, 18(2) (2008), 895-904.
  6. C. Faith, On K¨othe rings, Math. Ann., 164 (1966), 207-212.
  7. C. Faith, Algebra II, Ring Theory, Grundlehren der mathematischen Wis- senschaften 191, Springer-Verlag, 1976.
  8. F. Kasch, Modules and rings, Academic Press, London, 1982.
  9. T. Y. Lam, Lectures on Modules and Rings, Springer- Verlag, New York, 1999.
  10. A. Rosenberg and D. Zelinsky, Finiteness of the injective hull, Math. Z., 70 (1959), 372-378.
  11. R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, 1991. Alejandro Alvarado-Garc´ıa, C´esar Cejudo-Castilla, Hugo Alberto Rinc´on-Mej´ıa, Ivan Fernando Vilchis-Montalvo Departmento de Matem´aticas Facultad de Ciencias Universidad Nacional Aut´onoma de M´exico Circuito Exterior, C.U. M´exico, D.F. e-mails: [email protected] (A. Alvarado G.) [email protected] (C. Cejudo C.) [email protected] (H. A. Rinc´on M.) [email protected] (I.F. Vilchis M.)