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Category of Intuitionistic Fuzzy Modules

Author

Listed:
  • Poonam Kumar Sharma

    (Department of Mathematics, D.A.V. College, Jalandhar 144008, India)

  • Chandni

    (Research Scholar, Department of Mathematics, Lovely Professional University, Jalandhar 144402, India)

  • Nitin Bhardwaj

    (Department of Mathematics, Lovely Professional University, Jalandhar 144402, India)

Abstract

We study the relationship between the category of R -modules ( C R - M ) and the category of intuitionistic fuzzy modules ( C R − IFM ). We construct a category C Lat ( R − IFM ) of complete lattices corresponding to every object in C R − M and then show that, corresponding to each morphism in C R − M , there exists a contravariant functor from C R − IFM to the category C Lat (=union of all C Lat ( R − IFM ) , corresponding to each object in C R − M ) that preserve infima. Then, we show that the category C R − IFM forms a top category over the category C R − M . Finally, we define and discuss the concept of kernel and cokernel in C R − IFM and show that C R − IFM is not an Abelian Category.

Suggested Citation

  • Poonam Kumar Sharma & Chandni & Nitin Bhardwaj, 2022. "Category of Intuitionistic Fuzzy Modules," Mathematics, MDPI, vol. 10(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:399-:d:735688
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