SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 4

On retractability and its relationships with lattices associated to a ring

Rodrigo Domínguez-lópez(Universidad Nacional Autónomo de México)0000-0003-3053-4786
Oscar Alberto Garrido-jıménez(Universidad Nacional Autónomo de México)0000-0001-6748-9857
Hugo Alberto Rincon Mejia(Universidad Nacional Autónoma de México)0000-0002-1527-8879
Manuel Gerardo Zorrilla-noriega(Universidad Nacional Autónomo de México)0000-0001-7461-1806
Pages
—
Publication Date
2021-08-06
🏛️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)

In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this work is threefold.
📊
Key Findings & Data:First, we explore some relationships between retractability and some lattices of classes of modules.
💡
Conclusion & Impact:In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:left mod-retractable ring · parainjective module · paraprojective module

Abstract

The purpose of this work is threefold. First, we explore some relationships between retractability and some lattices of classes of modules. Secondly, we weaken the hypothesis of a result of Ohtake characterizing rings over which all radicals are left exact. In the last section of this work, we introduce a binary relation between modules that produce a Galois connection between the lattice of natural classes and the lattice of conatural classes, and we obtain some results about it.

🔖

Cite This Article

Domínguez-lópez, R., Garrido-jıménez, O. A., Mejia, H. A. R., Zorrilla-noriega, M. G. (2021). On retractability and its relationships with lattices associated to a ring. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 4. https://doi.org/10.15672/hujms.799818

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. A. Alvarado García, H. Rincón-Mejía and J. Ríos Montes, On the lattices of natural and conatural classes in R-Mod, Comm. Algebra, 29 (2), 541–556, 2001.
  2. A. Alvarado-García, C. Cejudo-Castilla, H. Rincón-Mejía and I.F. Vilchis-Montalvo, Pseudocomplements and strong pseudocomplements in lattices of module classes, J. Algebra Appl. 17 (1), 1850016, 2018.
  3. A. Alvarado-García, C. Cejudo-Castilla, H. Rincón-Mejía, I.F. Vilchis-Montalvo and M. Zorrilla-Noriega, On boolean lattices of module classes, Algebra Colloq. 25 (2), 285–294, 2018.
  4. F.W. Anderson and K.R. Fuller, Rings and Categories of Modules, Second edition, New York, Springer-Verlag, 1992.
  5. L. Bican, T. Kepka and P. Němec, Rings, Modules and Preradicals, New York, Marcel Dekker, 1982.
  6. K. Chiba and H. Tominaga, On strongly regular rings, Proc. Japan Acad. 49 (6), 435–437, 1973.
  7. J.H. Cozzens, Homological properties of the ring of differential polynomials, Bull. Amer. Math. Soc. 76 (1), 75–79, 1970.
  8. J. Dauns and Y. Zhou, Classes of Modules, Pure and Applied Mathematics, 281, Chapman & Hall/CRC, Boca Raton FL., 2006.
  9. R. Fernández-Alonso, F. Raggi, J. Ríos, H. Rincón-Mejía and C. Signoret, The lattice structure of preradicals II. Partitions, J. Algebra Appl. 1 (2), 201–214, 2002.
  10. J.S. Golan, Torsion Theories, in:Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 29, Longman Scientific and Technical, Harlow, John Wiley and Sons, New York, 1986.
  11. M.T. Koşan and J. Žemlička, Mod-Retractable Rings, Comm. Algebra, 42 (3), 998– 1010, 2014.
  12. K. Ohtake, Commutative rings of which all radicals are left exact, Comm. Algebra, 8 (16), 1505–1512, 1980.
  13. H. Rincón-Mejía and M. Zorrilla-Noriega, On some relations between the lattices Rnat, R-conat and R-tors and the rings they characterize, J. Algebra Appl. 12 (5), 2013.
  14. B. Stenström, Rings of Quotients, Berlin, Heidelberg, New York, Springer-Verlag, 1975.
  15. Y. Zhou, The lattice of natural classes of modules, Comm. Algebra, 24 (5), 1637–1648, 1996.