Volume 21, Issue 2 (9-2026)
IJMSI 2026, 21(2): 205-231 |
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Garrido-Jiménez O A, Rincón-Mejía H A. On σ-Classes of Modules with Applications. IJMSI 2026; 21 (2) :205-231
URL: http://ijmsi.ir/article-1-2324-en.html
URL: http://ijmsi.ir/article-1-2324-en.html
Abstract:
In this paper, we introduce some lattices of classes of left R-module relative to a preradical sigma. These lattices are generalizations of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theories, hereditary torsion theories, natural classes and conatural classes, respectively. We define the lattices σ-(R-TORS), σ-(R-tors), σ-(R-nat), σ-(R-conat), which reduce to the lattices mentioned above, when one takes sigma as the identity. We characterize the equality between these lattices by means of the (σ-HH) condition, which we introduce. We also present some results about σ-retractable rings, σ-Max rings extending results about Mod-retractable rings and Max rings.
Keywords: Preradical, Lattices of module classes, Left Mod-retractable ring, Left semiartinian ring, Left max ring.
Type of Study: Research paper |
Subject:
Special
References
1. A. Alvarado-Garc'ıa, C. Cejudo-Castilla, H. A. Rinc'on-Mej'ıa, I. F. Vilchis-Montalvo, M. Zorrilla-Noriega, On Boolean Lattices of Module Classes, Algebra Colloq., 25(2), (2018), 285-294. [DOI:10.1142/S1005386718000202]
2. A. Alvarado-Garc'ıa, C. Cejudo-Castilla, H. A. Rinc'on-Mej'ıa, I. F. Vilchis-Montalvo, Pseudocomplements and Strong Pseudocomplements in Lattices of Module Classes, J. Algebra Appl, 17(1), (2018), 1-14. [DOI:10.1142/S0219498818500160]
3. A. Alvarado Garc'ıa, H. A. Rinc'on-Mej'ıa, J. R'ıos Montes, On the Lattices of Natural and Conatural Classes in R-Mod, Comm. Algebra, 29(2), (2001), 541-556. [DOI:10.1081/AGB-100001523]
4. L. Bican, T. Kepka, P. Nˇemec, Rings, Modules and Preradicals, Marcel Dekker, New York, 1982.
5. E. Cerda-Le'on, H. A. Rinc'on-Mej'ıa, Big Lattices of Module Classes Induced by Preradicals, S˜ao Paulo J. Math. Sci., 14, (2020), 185-206. [DOI:10.1007/s40863-019-00160-5]
6. E. Cerda-Le'on, H. A. Rinc'on-Mej'ıa, On Lattices Associated to Rings with Respect to a Preradical, Int. Electron. J. Algebra, 31, (2022), 13-37. [DOI:10.24330/ieja.1058385]
7. J. Dauns, Y. Zhou, Classes of Modules, Chapman & Hall/CRC, Boca Raton FL., 2006. [DOI:10.1201/9781420011593]
8. R. Dom'ınguez-L'opez, O. A. Garrido-Jim'enez, H. A. Rinc'on-Mej'ıa, M. Zorrilla-Noriega, On Retractability and its Relationships with Lattices Associated to a Ring, Hacet. J. Math. Stat., 50(4), (2021), 1079-1093. [DOI:10.15672/hujms.799818]
9. J. S. Golan, Torsion Theories, John Wiley and Sons, New York, 1986.
10. M. T. Ko¸san, J. Zemliˇcka, Mod-retractable Rings, ˇ Comm. Algebra, 42(3), (2014), 998-1010. [DOI:10.1080/00927872.2012.721430]
11. F. Raggi, J. R'ıos, Algunas Relaciones Entre Anillos Semiartinianos y la teor'ıa de torsi'on de Goldie, An. Inst. Mat. Univ. Nac. Aut'onoma M'exico, 23, (1983), 41-54.
12. H. A. Rinc'on-Mej'ıa, The Lattice R-tors for Perfect Rings, Publicacions Matematiques, 33, (1989), 17-35. [DOI:10.5565/PUBLMAT_33189_02]
13. B. Stenstr¨om , Rings of quotients, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
14. B. Talaee, A Generalization of M-small Modules, Journal of Sciences, Islamic Republic of Iran, 26(2), (2015), 179-185.
15. B. Talaee, G-δ-M Modules and Torsion Theories Cogenerated by Such Modules, Iranian Journal of Science and Technology, Transactions A: Science, 42, (2018), 141-146. [DOI:10.1007/s40995-017-0239-4]
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