Some topological properties of spectrum of intuitionistic fuzzy prime submodules
Downloads
DOI:
https://doi.org/10.26637/MJM0804/0004Abstract
collection of all intuitionistic fuzzy prime submodules of \(M\). In this regards some basic properties of Zariski topology on IFSpec(M) are investigated. In particular, we prove some equivalent conditions for irreducible subsets of this topological space and it is shown under certain conditions \(I F S p e c(M)\) is a \(T_0\)-space or Hausdorff.
Keywords:
Intuitionistic fuzzy prime submodules, Intuitionistic fuzzy prime Spectrum, top modules, Zariski topologyMathematics Subject Classification:
Mathematics- Pages: 1363-1369
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
I. Bakhadach, S., Melliani, M., Oukessou and S.L., Chadli, Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring, Notes on Intuitionistic Fuzzy Sets, $22(2)(2016), 59-63$.
D.K. Basnet, Topics in Intuitionistic Fuzzy Algebra, , Lambert Academic Publishing, (2011).
B. Davvaz, W.A., Dudek, Y.B., Jun, Intuitionistic fuzzy Hv-submodules, Information Sciences, 176 (2006), 285 300 .
P. Isaac, and P.P.,John, On intuitionistic fuzzy submodules of a modules, International Journal of Mathematical Sciences and Applications, 1(3)(2011), 1447-1454.
${ }^{[5]}$ H.V. Kumbhojkar, Spectrum of prime fuzzy ideals, Fuzzy Sets and Systems, 62(1994), 101-109.
C. P. Lu, The Zariski topology on the Prime Spectrum of a Module, Houston J. Math., 25(3)(1999), 417-425.
R.L. McCasland, M.E., Moore, Prime submodules, Comm. Algebra, 20(1992), 1803-1817.
R.L. McCasland, M.E., Moore, and P.F., Smith, On the spectrum of a module over a commutative ring, Comm. Algebra, 25(1)(1997), 79-103.
S. Rahman, and H.K., Saikia, Some Aspects of Atanassov's Intuitionistic Fuzzy Submodules, International Journal of Pure and Applied Mathematics, $77(3)(2012), 369-383$.
P.K. Sharma, $(alpha, beta)$-cut of intuitionistic fuzzy modules, International Journal of Mathematical Sciences and Applications, 1(3) (2011), 1489-1492.
P.K. Sharma, G., Kaur, On intuitionistic fuzzy prime submodules, Notes on Intuitionistic Fuzzy Sets, 24(4)(2018), $97-112$.
P.K. Sharma, Kanchan, On intuitionistic L-fuzzy prime submodules, Annals of Fuzzy Mathematics and Informatics, 16(1)(2018), 87-97.
P.K. Sharma, and G., Kaur, Residual quotient and annihilator of intuitionistic fuzzy sets of ring and module, International Journal of Computer Science and Information Technology, 9(4)(2017), 1-15.
P.K. Sharma, and G., Kaur, Intuitionistic fuzzy prime spectrum of a ring, International Journal of Fuzzy Systems, 9(8) (2017), 167-175.
P.K. Sharma, and G., Kaur, On annihilator of intuitionistic fuzzy subsets of modules, Proceeding of Third International Conference on Fuzzy Logic Systems (Fuzzy-2017) held at Chenai, India from 29-30 ${ }^{text {th }}$ July,2017, proceeding published by DhinaharanNagamalai et al. (Eds) : SIGEM, CSEA, Fuzzy, NATL - 2017, pp. 37- 49, 2017. DOI : $10.5121 / mathrm{csit} .2017 .70904$.
P.K. Sharma, Kanchan, The Zariski topology on the spectrum of intuitionistic $L$ - fuzzy prime submodules, Communicated.
H. A. Toroghy, and R. O., Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Communications in Algebra, 38 (2010), 4461-4475.
- NA
Similar Articles
- K. Manikandan, S. Moidhen Aliyar, S. Manimaran, An equitable edge coloring of some classes of product of graphs , Malaya Journal of Matematik: Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.