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Dual Zariski Topology on Comultiplication Modules

Yıl 2019, Cilt: 23 Sayı: 3, 390 - 395, 01.06.2019
https://doi.org/10.16984/saufenbilder.459289

Öz

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 XsN 
is an Artinian topological space if and only if M satisfies
the SN-condition.

Kaynakça

  • R. Ameri, “Some properties of Zariski topology of multiplication modules”, Houston Journal of Mathematics, vol. 36, pp. 337-344, 2010.
  • H. Ansari-Toroghy and F. Farshadifar, “On the Dual Notion of Prime Submodules,” Algebra Colloquium, vol. 19, no. 1, pp. 1109–1116, 2012.
  • 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.
  • N. Bourbaki, “Elements of Mathematics General Topology Part 1 and Part 2,” Hermann and Addison-Wesley, Paris, 1966.
  • 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.
  • S. Çeken and M. Alkan, “Dual of Zariski topology for modules,” Book Series: AIP Conf. Proc., vol. 1389, no. 1, pp. 357–360, 2013.
  • Z. El-Bast and P. F. Smith, “Multiplications Modules,” Comm. in Algebra, vol. 16, pp. 755-779, 1998.
  • 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.
  • R. Y. Sharp, “Steps in commutative algebra,” Cambridge University Press, Cambridge, 2001.
  • 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.
  • O. Öneş and M. Alkan, “Zariski Subspace Topologies On Ideals,” Hacettepe Journal of Mathematics and Statistics, accepted, Doi: 10.15672/HJMS.2018.597, 2018.
  • 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.
  • S. Yassemi, “The dual notion of prime submodules,” Arch. Math. (Brno), vol. 37, pp. 273–278, 2001.
Yıl 2019, Cilt: 23 Sayı: 3, 390 - 395, 01.06.2019
https://doi.org/10.16984/saufenbilder.459289

Öz

Kaynakça

  • R. Ameri, “Some properties of Zariski topology of multiplication modules”, Houston Journal of Mathematics, vol. 36, pp. 337-344, 2010.
  • H. Ansari-Toroghy and F. Farshadifar, “On the Dual Notion of Prime Submodules,” Algebra Colloquium, vol. 19, no. 1, pp. 1109–1116, 2012.
  • 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.
  • N. Bourbaki, “Elements of Mathematics General Topology Part 1 and Part 2,” Hermann and Addison-Wesley, Paris, 1966.
  • 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.
  • S. Çeken and M. Alkan, “Dual of Zariski topology for modules,” Book Series: AIP Conf. Proc., vol. 1389, no. 1, pp. 357–360, 2013.
  • Z. El-Bast and P. F. Smith, “Multiplications Modules,” Comm. in Algebra, vol. 16, pp. 755-779, 1998.
  • 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.
  • R. Y. Sharp, “Steps in commutative algebra,” Cambridge University Press, Cambridge, 2001.
  • 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.
  • O. Öneş and M. Alkan, “Zariski Subspace Topologies On Ideals,” Hacettepe Journal of Mathematics and Statistics, accepted, Doi: 10.15672/HJMS.2018.597, 2018.
  • 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.
  • S. Yassemi, “The dual notion of prime submodules,” Arch. Math. (Brno), vol. 37, pp. 273–278, 2001.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Ortaç Öneş 0000-0001-6777-9192

Yayımlanma Tarihi 1 Haziran 2019
Gönderilme Tarihi 12 Eylül 2018
Kabul Tarihi 20 Aralık 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 23 Sayı: 3

Kaynak Göster

APA Öneş, O. (2019). Dual Zariski Topology on Comultiplication Modules. Sakarya University Journal of Science, 23(3), 390-395. https://doi.org/10.16984/saufenbilder.459289
AMA Öneş O. Dual Zariski Topology on Comultiplication Modules. SAUJS. Haziran 2019;23(3):390-395. doi:10.16984/saufenbilder.459289
Chicago Öneş, Ortaç. “Dual Zariski Topology on Comultiplication Modules”. Sakarya University Journal of Science 23, sy. 3 (Haziran 2019): 390-95. https://doi.org/10.16984/saufenbilder.459289.
EndNote Öneş O (01 Haziran 2019) Dual Zariski Topology on Comultiplication Modules. Sakarya University Journal of Science 23 3 390–395.
IEEE O. Öneş, “Dual Zariski Topology on Comultiplication Modules”, SAUJS, c. 23, sy. 3, ss. 390–395, 2019, doi: 10.16984/saufenbilder.459289.
ISNAD Öneş, Ortaç. “Dual Zariski Topology on Comultiplication Modules”. Sakarya University Journal of Science 23/3 (Haziran 2019), 390-395. https://doi.org/10.16984/saufenbilder.459289.
JAMA Öneş O. Dual Zariski Topology on Comultiplication Modules. SAUJS. 2019;23:390–395.
MLA Öneş, Ortaç. “Dual Zariski Topology on Comultiplication Modules”. Sakarya University Journal of Science, c. 23, sy. 3, 2019, ss. 390-5, doi:10.16984/saufenbilder.459289.
Vancouver Öneş O. Dual Zariski Topology on Comultiplication Modules. SAUJS. 2019;23(3):390-5.