SavedAdd your journal

Journals / International Electronic Journal of Algebra / 2026 / Volume: 37 Issue: 37

Artinian* Modules

Ajim Uddin Ansari(University of Allahabad)
Hwankoo Kim(Hoseo University)
Sanjeev Kumar Maurya(Galgotias University)
Ünsal Tekir(Marmara University)
Pages
—
Publication Date
2025-01-14
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we characterize Artinian* modules in the amalgamated module construction.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce and study Artinian* modules as a generalization of Artinian modules.
📊
Key Findings & Data:We transfer several results of Artinian modules to Artinian* modules.
💡
Conclusion & Impact:Finally, we characterize Artinian* modules in the amalgamated module construction.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Artinian ring · Artinian module · Artinian* ring

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.

🔖

Cite This Article

Ansari, A. U., Kim, H., Maurya, S. K., Tekir, Ü. (2025). Artinian* Modules. International Electronic Journal of Algebra, Volume: 37 Issue: 37. https://doi.org/10.24330/ieja.1571460

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. D. D. Anderson, T. Arabacı, Ü. Tekir and S. Koç, On $S$-multiplication modules, Comm. Algebra, 48(8) (2020), 3398-3407.
  2. D. F. Anderson and A. Badawi, Von Neumann regular and related elements in commutative rings, Algebra Colloq., 19(1) (2012), 1017-1040.
  3. A. U. Ansari and B. K. Sharma, Graded $S$-Artinian modules and graded $S$-secondary representations, Palest. J. Math., 11(3) (2022), 175-193.
  4. E. Artin, Zur Theorie der hyperkomplexen Zahlen, Abh. Math. Sem. Univ. Hamburg, 5(1) (1927), 251-260.
  5. S. E. Atani, Submodules of secondary modules, Int. J. Math. Math. Sci., 31(6) (2002), 321-327.
  6. M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969.
  7. A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
  8. 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.
  9. Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
  10. R. El Khalfaoui, N. Mahdou, P. Sahandi and N. Shirmohammadi, Amalgamated modules along an ideal, Commun. Korean Math. Soc., 36(1) (2021), 1-10.
  11. A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism, J. Algebra, 453 (2016), 578-601.
  12. C. Jayaram, K. H. Oral and Ü. Tekir, Strongly 0-dimensional rings, Comm. Algebra, 41(6) (2013), 2026-2032.
  13. O. Khani-Nasab and A. Hamed, Weakly $S$-Artinian modules, Filomat, 35(15) (2021), 5215-5226.
  14. I. G. Macdonald, Secondary representation of modules over a commutative rings, Symposia Mathematica, 11 (1973), 23-43.
  15. 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.
  16. 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).