Abstract
References
- D. D. Anderson, T. Arabacı, Ü. Tekir and S. Koç, On $S$-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
- D. F. Anderson and A. Badawi, Von Neumann regular and related elements in commutative rings, Algebra Colloq., 19(1) (2012), 1017-1040.
- A. U. Ansari and B. K. Sharma, Graded $S$-Artinian modules and graded $S$-secondary representations, Palest. J. Math., 11(3) (2022), 175-193.
- E. Artin, Zur Theorie der hyperkomplexen Zahlen, Abh. Math. Sem. Univ. Hamburg, 5(1) (1927), 251-260.
- S. E. Atani, Submodules of secondary modules, Int. J. Math. Math. Sci., 31(6) (2002), 321-327.
- M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.
- A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
- M. D'Anna, C. A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, Commutative Algebra and its Applications: Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Fez, Morocco, June 23-28, 2008, edited by M. Fontana, S. E. Kabbaj, B. Olberding and I. Swanson, Berlin, New York: De Gruyter, 2009, 155-172.
- Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
- R. El Khalfaoui, N. Mahdou, P. Sahandi and N. Shirmohammadi, Amalgamated modules along an ideal, Commun. Korean Math. Soc., 36(1) (2021), 1-10.
- A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism, J. Algebra, 453 (2016), 578-601.
- C. Jayaram, K. H. Oral and Ü. Tekir, Strongly 0-dimensional rings, Comm. Algebra, 41(6) (2013), 2026-2032.
- O. Khani-Nasab and A. Hamed, Weakly $S$-Artinian modules, Filomat, 35(15) (2021), 5215-5226.
- I. G. Macdonald, Secondary representation of modules over a commutative rings, Symposia Mathematica, 11 (1973), 23-43.
- M. Özen, O. A. Naji, Ü. Tekir and K. P. Shum, Characterization theorems of $S$-Artinian modules, C. R. Acad. Bulgare Sci., 74(4) (2021), 496-505.
- E. S. Sevim, Ü. Tekir and S. Koç, $S$-Artinian rings and finitely $S$-cogenerated rings, J. Algebra Appl., 19(3) (2020), 2050051 (16 pp).
Abstract
In this paper, we introduce and study Artinian* modules as a generalization of Artinian modules. We transfer several results of Artinian modules to Artinian* modules. We also provide several characterizations of this new class of modules. Furthermore, we investigate the existence of secondary representation for Artinian* modules over commutative regular rings. Finally, we characterize Artinian* modules in the amalgamated module construction.
Keywords
Artinian ring Artinian module Artinian* ring Artinian* module secondary representable module
References
- D. D. Anderson, T. Arabacı, Ü. Tekir and S. Koç, On $S$-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
- D. F. Anderson and A. Badawi, Von Neumann regular and related elements in commutative rings, Algebra Colloq., 19(1) (2012), 1017-1040.
- A. U. Ansari and B. K. Sharma, Graded $S$-Artinian modules and graded $S$-secondary representations, Palest. J. Math., 11(3) (2022), 175-193.
- E. Artin, Zur Theorie der hyperkomplexen Zahlen, Abh. Math. Sem. Univ. Hamburg, 5(1) (1927), 251-260.
- S. E. Atani, Submodules of secondary modules, Int. J. Math. Math. Sci., 31(6) (2002), 321-327.
- M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.
- A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
- M. D'Anna, C. A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, Commutative Algebra and its Applications: Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, Fez, Morocco, June 23-28, 2008, edited by M. Fontana, S. E. Kabbaj, B. Olberding and I. Swanson, Berlin, New York: De Gruyter, 2009, 155-172.
- Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
- R. El Khalfaoui, N. Mahdou, P. Sahandi and N. Shirmohammadi, Amalgamated modules along an ideal, Commun. Korean Math. Soc., 36(1) (2021), 1-10.
- A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism, J. Algebra, 453 (2016), 578-601.
- C. Jayaram, K. H. Oral and Ü. Tekir, Strongly 0-dimensional rings, Comm. Algebra, 41(6) (2013), 2026-2032.
- O. Khani-Nasab and A. Hamed, Weakly $S$-Artinian modules, Filomat, 35(15) (2021), 5215-5226.
- I. G. Macdonald, Secondary representation of modules over a commutative rings, Symposia Mathematica, 11 (1973), 23-43.
- M. Özen, O. A. Naji, Ü. Tekir and K. P. Shum, Characterization theorems of $S$-Artinian modules, C. R. Acad. Bulgare Sci., 74(4) (2021), 496-505.
- E. S. Sevim, Ü. Tekir and S. Koç, $S$-Artinian rings and finitely $S$-cogenerated rings, J. Algebra Appl., 19(3) (2020), 2050051 (16 pp).
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Research Article |
| Authors | |
| Submission Date | March 8, 2024 |
| Acceptance Date | July 26, 2024 |
| Early Pub Date | October 21, 2024 |
| Publication Date | January 14, 2025 |
| DOI | https://doi.org/10.24330/ieja.1571460 |
| IZ | https://izlik.org/JA58JU77GL |
| Published in Issue | Year 2025 Volume: 37 Issue: 37 |