KaydedilenlerDerginizi ekleyin

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

Dual Zariski Topology on Comultiplication Modules

Ortaç Öneş(AKDENIZ UNIVERSITY)0000-0001-6777-9192
Sayfa
—
Yayın Tarihi
2019-06-01
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper deals with dual Zariski topology on comultiplication modules.
📊
Temel Bulgular & Veri:We define a subspace topology of dual Zariski topology on comultiplication modules and study some properties of this subspace topology.
💡
Sonuç & Katkı:We prove that X s N is an Artinian topological space if and only if M satisfies the SN-condition.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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.