Research Article
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Year 2024, Early Access, 1 - 20
https://doi.org/10.24330/ieja.1476650

Abstract

References

  • J. Abuhlail and H. Hroub, PS-hollow representations of modules over commutative rings, J. Algebra Appl., 21 (2022), 2250243 (18 pp).
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • L. Bican, T. Kepka and P. Nˇemec, Rings, Modules, and Preradicals, Lecture Notes in Pure and Applied Mathematics, 75, Marcel Dekker, Inc., New York, 1982.
  • S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41(1) (2013), 83-98.
  • J. S. Golan, Torsion Theories, Pitman Monographs and Surveys in Pure and Applied Mathematics, 29, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986.
  • F. Raggi, J. R. Montes, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra, 30(3) (2002), 1533-1544.
  • F. Raggi, J. R. Montes, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals II. Partitions, J. Algebra Appl., 1(2) (2002), 201-214.
  • F. Raggi, J. R. Montes, H. Rinc´on, R. Fern´andez-Alonso and C. Signoret, The lattice structure of preradicals III. Operators, J. Pure Appl. Algebra, 190 (2004), 251-265.
  • B. Stenstrom, Rings of Quotients, An introduction to methods of ring theory, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer-Verlag, New York-Heidelberg, 1975.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37 (2001), 273-278.

Second modules relative to subclasses of preradicals of $R$-Mod

Year 2024, Early Access, 1 - 20
https://doi.org/10.24330/ieja.1476650

Abstract

We study the concept of second module and extend it to more general environments. We also provide descriptions of simple left semiartinian, left local rings, semisimple and simple rings in terms of their $\mathscr A$-second modules with respect to a preradical class.

References

  • J. Abuhlail and H. Hroub, PS-hollow representations of modules over commutative rings, J. Algebra Appl., 21 (2022), 2250243 (18 pp).
  • F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
  • L. Bican, T. Kepka and P. Nˇemec, Rings, Modules, and Preradicals, Lecture Notes in Pure and Applied Mathematics, 75, Marcel Dekker, Inc., New York, 1982.
  • S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41(1) (2013), 83-98.
  • J. S. Golan, Torsion Theories, Pitman Monographs and Surveys in Pure and Applied Mathematics, 29, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986.
  • F. Raggi, J. R. Montes, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra, 30(3) (2002), 1533-1544.
  • F. Raggi, J. R. Montes, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals II. Partitions, J. Algebra Appl., 1(2) (2002), 201-214.
  • F. Raggi, J. R. Montes, H. Rinc´on, R. Fern´andez-Alonso and C. Signoret, The lattice structure of preradicals III. Operators, J. Pure Appl. Algebra, 190 (2004), 251-265.
  • B. Stenstrom, Rings of Quotients, An introduction to methods of ring theory, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer-Verlag, New York-Heidelberg, 1975.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37 (2001), 273-278.
There are 10 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Luis Fernando García Mora

Hugo Alberto Rincon Mejia

Early Pub Date May 2, 2024
Publication Date
Published in Issue Year 2024 Early Access

Cite

APA García Mora, L. F., & Rincon Mejia, H. A. (2024). Second modules relative to subclasses of preradicals of $R$-Mod. International Electronic Journal of Algebra1-20. https://doi.org/10.24330/ieja.1476650
AMA García Mora LF, Rincon Mejia HA. Second modules relative to subclasses of preradicals of $R$-Mod. IEJA. Published online May 1, 2024:1-20. doi:10.24330/ieja.1476650
Chicago García Mora, Luis Fernando, and Hugo Alberto Rincon Mejia. “Second Modules Relative to Subclasses of Preradicals of $R$-Mod”. International Electronic Journal of Algebra, May (May 2024), 1-20. https://doi.org/10.24330/ieja.1476650.
EndNote García Mora LF, Rincon Mejia HA (May 1, 2024) Second modules relative to subclasses of preradicals of $R$-Mod. International Electronic Journal of Algebra 1–20.
IEEE L. F. García Mora and H. A. Rincon Mejia, “Second modules relative to subclasses of preradicals of $R$-Mod”, IEJA, pp. 1–20, May 2024, doi: 10.24330/ieja.1476650.
ISNAD García Mora, Luis Fernando - Rincon Mejia, Hugo Alberto. “Second Modules Relative to Subclasses of Preradicals of $R$-Mod”. International Electronic Journal of Algebra. May 2024. 1-20. https://doi.org/10.24330/ieja.1476650.
JAMA García Mora LF, Rincon Mejia HA. Second modules relative to subclasses of preradicals of $R$-Mod. IEJA. 2024;:1–20.
MLA García Mora, Luis Fernando and Hugo Alberto Rincon Mejia. “Second Modules Relative to Subclasses of Preradicals of $R$-Mod”. International Electronic Journal of Algebra, 2024, pp. 1-20, doi:10.24330/ieja.1476650.
Vancouver García Mora LF, Rincon Mejia HA. Second modules relative to subclasses of preradicals of $R$-Mod. IEJA. 2024:1-20.