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Issue:On decomposition of intuitionistic fuzzy prime submodules: Difference between revisions

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  | author          = P. K. Sharma
  | author          = P. K. Sharma
  | institution    = Post Graduate Department of Mathematics, D.A.V. College
  | institution    = Post Graduate Department of Mathematics, D.A.V. College
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  | format          = PDF
  | format          = PDF
  | size            = 167
  | size            = 167
  | abstract        = In this paper, the concepts of intuitionistic fuzzy Mengerness, intuitionistic fuzzy near Mengerness and intuitionistic fuzzy almost Mengerness are introduced and studied. We give some characterizations of intuitionistic fuzzy almost Mengerness in terms of intuitionistic fuzzy regular open or intuitionistic fuzzy regular closed.
  | abstract        = This article is in continuation of the first author’s previous paper on intuitionistic fuzzy prime submodules, [13]. In this paper, we explore the decomposition of intuitionistic fuzzy submodule as the intersection of finite many intuitionistic fuzzy prime submodules. Many other forms of decomposition like irredundant and normal decomposition are also investigated.
 
  | keywords        = Intuitionistic fuzzy prime ideal (submodule), Residual quotient, Intuitionistic fuzzy prime decomposition, Irredundant and normal decomposition.
  | keywords        = Intuitionistic fuzzy topology, Intuitionistic fuzzy Menger spaces, Intuitionistic fuzzy near Menger spaces, Intuitionistic fuzzy almost Menger spaces.
  | ams            = 03F55, 16D10, 46J20.
  | ams            = 54A40, 03E72.
  | references      =  
  | references      =  


Latest revision as of 08:26, 5 October 2020

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http://ifigenia.org/wiki/issue:nifs/26/2/25-32
Title of paper: On decomposition of intuitionistic fuzzy prime submodules
Author(s):
P. K. Sharma
Post Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Kanchan
Research Scholar, IKG PT University, Jalandhar, Punjab, India
kanchan4usoh@gmail.com
D. S. Pathania
Department of Applied Sciences, GNDEC, Ludhiana, Punjab, India
despathania@yahoo.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 26 (2020), Number 2, pages 25–32
DOI: https://doi.org/10.7546/nifs.2020.26.2.25-32
Download:  PDF (167  Kb, Info)
Abstract: This article is in continuation of the first author’s previous paper on intuitionistic fuzzy prime submodules, [13]. In this paper, we explore the decomposition of intuitionistic fuzzy submodule as the intersection of finite many intuitionistic fuzzy prime submodules. Many other forms of decomposition like irredundant and normal decomposition are also investigated.
Keywords: Intuitionistic fuzzy prime ideal (submodule), Residual quotient, Intuitionistic fuzzy prime decomposition, Irredundant and normal decomposition.
AMS Classification: 03F55, 16D10, 46J20.
References:
  1. Akray, I., & Hussein, H. S. (2017). I-Prime Submodules, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 33, 165–173.
  2. Amini, A., Amini, B. & Sharif, H. (2006). Prime and primary submodule of certain modules, Czechoslovak Mathematical Journal, 56 (131), 641–648.
  3. Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1), 87–96.
  4. Bakhadach, I., Melliani, S. Oukessou, M., & Chadli, L. S. (2016). Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring, Notes on Intuitionistic Fuzzy Sets, 22 (2), 59–63.
  5. Basnet, D. K. (2011). Topics in Intuitionistic Fuzzy Algebra, Lambert Academic Publishing, ISBN: 978-3-8443-9147-3.
  6. Meena, K., & Thomas, K. V. (2011). Intuitionistic L-Fuzzy Subrings, International Mathematical Forum, 6 (52), 2561–2572.
  7. Lu, C. P. (1984). Prime Submodules of Modules, Comment. Math. Univ. Sancti Paulli, 33 (1), 61–69.
  8. McCasland, R. L., & Moore, M. E. (1992). Prime Submodules, Comm. Algebra, 20 (6), 1803–1817.
  9. Tiras¸, Y. & Harmanci, A. (2000). On Prime Submodules and Primary Decomposition, Czech. Math. J., 50 (125), 83–90.
  10. Sharma, P. K. (2016). Reducibility and Complete Reducibility of intuitionistic fuzzy G-modules, Annals of Fuzzy Mathematics and Informatics, 11 (6), 885–898.
  11. Sharma P. K., & Kaur, G. (2017). Residual quotient and annihilator of intuitionistic fuzzy sets of ring and module, International Journal of Computer Sciences and Information Techonology, 9 (4), 1–15.
  12. Sharma P. K., & Kaur, G. (2017). Intuitionistic fuzzy prime spectrum of a ring, CiiT International Journal of Fuzzy Systems, 9 (8), 167–175.
  13. Sharma P. K., & Kaur, G. (2018). On intuitionistic fuzzy prime submodules, Notes on Intuitionistic Fuzzy Sets, 24 (4), 97–112.
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