Öz
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
R-pr A-second module strongly second module left semiartinian left local ring
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 2 Mayıs 2024 |
| Yayımlanma Tarihi | 12 Temmuz 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 36 Sayı: 36 |