Dual Zariski Topology on Comultiplication Modules

Yıl 2019, , 390 - 395, 01.06.2019

Ortaç Öneş

https://doi.org/10.16984/saufenbilder.459289

Cited By: 1

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 X^s_N is an Artinian topological space if and only if M satisfies
the SN-condition.

Anahtar Kelimeler

Comultiplication Modules, Dual Zariski Topology, Second Module

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.