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

Year 2024, Volume: 36 Issue: 36, 101 - 120, 12.07.2024

Luis Fernando García Mora , Hugo Alberto Rincon Mejia

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.

Keywords

R-pr, A-second module, strongly second module, left semiartinian, left local ring

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.