The Universal Coefticient Theorem in the Category of Fuzzy Soft Modules

Sebuhi Abdullayev; S. A. Bayramov

doi:10.24297/jam.v14i2.7599

Authors

Sebuhi Abdullayev Baku State University, Baku, Azerbaijan
S. A. Bayramov Baku State University, Baku, Azerbaijan

DOI:

https://doi.org/10.24297/jam.v14i2.7599

Keywords:

Universal Coefticient Theorem, Soft Module, Fuzzy Soft Module, Chain Complex Of Fuzzy Soft Modules, Short Exact Sequence Fuzzy Soft Modules

Abstract

This paper begins with the basic concepts of chain comlexes of fuzzy soft modules. Later, we introduce short exact sequence of fuzzy soft modules and prove that split short exact sequence of fuzzy soft chain complex. Naturally, we want to investigate whether or not the universal coefficient theorems are satisfied in category of fuzzy soft chain complexes. However, in the proof of these theorems in the category of chain complexes, exact sequence of homology modules of chain complexes is used. Generally, sequence of fuzzy soft homology modules is not exact in fuzzy chain complexes. Therefore in this study, we construct exact sequence of fuzzy soft homology modules under some conditions. Universal coefficients theorem is proven by making use of this idea.

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Author Biographies

Sebuhi Abdullayev, Baku State University, Baku, Azerbaijan

Department of Algebra and Geometry, Baku State University, 23,, Z.Khalilov str.,, AZ1148, Baku, Azerbaijan

S. A. Bayramov, Baku State University, Baku, Azerbaijan

Department of Algebra and Geometry, Baku State University, 23,, Z.Khalilov str.,, AZ1148, Baku, Azerbaijan

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