Second modules relative to subclasses of preradicals of $R$-Mod-Reference-Cited by-同舟云学术

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

Published:2024-07-12 Issue:36 Volume:36 Page:101-120
ISSN:1306-6048
Container-title:International Electronic Journal of Algebra
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Author:

García Mora Luis Fernando¹,Rincon Mejia Hugo Alberto¹

Affiliation:

1. Universidad Nacional Autonoma de Mexico

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.

Publisher

The International Electronic Journal of Algebra

Reference10 articles.

1. J. Abuhlail and H. Hroub, PS-hollow representations of modules over commutative rings, J. Algebra Appl., 21 (2022), 2250243 (18 pp).

2. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.

3. 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.

4. S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41(1) (2013), 83-98.

5. 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.

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