Research Article

Dual Zariski Topology on Comultiplication Modules

Volume: 23 Number: 3 June 1, 2019
EN

Dual Zariski Topology on Comultiplication Modules

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

Keywords

References

  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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

June 1, 2019

Submission Date

September 12, 2018

Acceptance Date

December 20, 2018

Published in Issue

Year 2019 Volume: 23 Number: 3

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
1.Öneş O. Dual Zariski Topology on Comultiplication Modules. SAUJS. 2019;23(3):390-395. doi:10.16984/saufenbilder.459289
Chicago
Öneş, Ortaç. 2019. “Dual Zariski Topology on Comultiplication Modules”. Sakarya University Journal of Science 23 (3): 390-95. https://doi.org/10.16984/saufenbilder.459289.
EndNote
Öneş O (June 1, 2019) Dual Zariski Topology on Comultiplication Modules. Sakarya University Journal of Science 23 3 390–395.
IEEE
[1]O. Öneş, “Dual Zariski Topology on Comultiplication Modules”, SAUJS, vol. 23, no. 3, pp. 390–395, June 2019, doi: 10.16984/saufenbilder.459289.
ISNAD
Öneş, Ortaç. “Dual Zariski Topology on Comultiplication Modules”. Sakarya University Journal of Science 23/3 (June 1, 2019): 390-395. https://doi.org/10.16984/saufenbilder.459289.
JAMA
1.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, vol. 23, no. 3, June 2019, pp. 390-5, doi:10.16984/saufenbilder.459289.
Vancouver
1.Ortaç Öneş. Dual Zariski Topology on Comultiplication Modules. SAUJS. 2019 Jun. 1;23(3):390-5. doi:10.16984/saufenbilder.459289

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