SavedAdd your journal

Journals / Sakarya University Journal of Science / 2026 / Volume: 23 Issue: 3

Dual Zariski Topology on Comultiplication Modules

Ortaç Öneş(AKDENIZ UNIVERSITY)0000-0001-6777-9192
Pages
—
Publication Date
2019-06-01
🏛️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)

We prove that X s N is an Artinian topological space if and only if M satisfies the SN-condition.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper deals with dual Zariski topology on comultiplication modules.
📊
Key Findings & Data:We define a subspace topology of dual Zariski topology on comultiplication modules and study some properties of this subspace topology.
💡
Conclusion & Impact:We prove that X s N is an Artinian topological space if and only if M satisfies the SN-condition.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Comultiplication Modules · Dual Zariski Topology · Second Module

Abstract

This paper deals with dual Zariski topology on comultiplication modules. We define a subspace topology of dual Zariski topology on comultiplication modules and study some properties of this subspace topology. We prove that X s N is an Artinian topological space if and only if M satisfies the SN-condition.

🔖

Cite This Article

Öneş, O. (2019). Dual Zariski Topology on Comultiplication Modules. Sakarya University Journal of Science, Volume: 23 Issue: 3. https://doi.org/10.16984/saufenbilder.459289

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. R. Ameri, “Some properties of Zariski topology of multiplication modules”, Houston Journal of Mathematics, vol. 36, pp. 337-344, 2010.
  2. H. Ansari-Toroghy and F. Farshadifar, “On the Dual Notion of Prime Submodules,” Algebra Colloquium, vol. 19, no. 1, pp. 1109–1116, 2012.
  3. H. Ansari-Toroghy and F. Farshadifar, “The Zariski Topology on the Second Spectrum of a Module,” Algebra Colloquium, vol. 21, no. 4, pp. 671–688, 2014.
  4. N. Bourbaki, “Elements of Mathematics General Topology Part 1 and Part 2,” Hermann and Addison-Wesley, Paris, 1966.
  5. S. Çeken and M. Alkan, “On the second Spectrum and the Second Classical Zariski topology of a Module,” Journal of Algebra and Its Applications, vol. 14, no. 8, pp. 1550150(1)–1550150(13), 2015.
  6. S. Çeken and M. Alkan, “Dual of Zariski topology for modules,” Book Series: AIP Conf. Proc., vol. 1389, no. 1, pp. 357–360, 2013.
  7. Z. El-Bast and P. F. Smith, “Multiplications Modules,” Comm. in Algebra, vol. 16, pp. 755-779, 1998.
  8. C. P. Lu, “The Zariski topology on the prime spectrum of a module,” Houston Journal of Mathematics, vol. 25, no. 3, pp. 417-432, 1999.
  9. R. Y. Sharp, “Steps in commutative algebra,” Cambridge University Press, Cambridge, 2001.
  10. O. Öneş and M. Alkan, “The structure of some topologies on modules,” AIP Conference Proceedings, vol. 1863, no. 1, pp. 300010(1)- 300010(4), 2017.
  11. O. Öneş and M. Alkan, “Zariski Subspace Topologies On Ideals,” Hacettepe Journal of Mathematics and Statistics, accepted, Doi: 10.15672/HJMS.2018.597, 2018.
  12. O. Öneş and M. Alkan, “The relationships between graded ideals and subspaces,” AIP Conference Proceedings, vol. 1991, no. 1, pp. 020027(1)- 020027(4), 2018.
  13. S. Yassemi, “The dual notion of prime submodules,” Arch. Math. (Brno), vol. 37, pp. 273–278, 2001.