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A new type fuzzy module over fuzzy rings
1Department of Mathematics, Faculty of Sciences and Arts, Marmara University, İstanbul, Turkey.
Thescientificworldjournal
|April 17, 2014
Summary
This study introduces a novel fuzzy module over a fuzzy ring, extending existing theories. Basic properties of fuzzy submodules and homomorphisms are explored, mirroring classical module theory.
Area of Science:
- Abstract Algebra
- Fuzzy Mathematics
Background:
- Generalizes existing definitions of fuzzy groups and fuzzy rings.
- Builds upon foundational concepts in abstract algebra and fuzzy set theory.
Purpose of the Study:
- Introduce a new structure: fuzzy modules over fuzzy rings.
- Investigate the fundamental properties of fuzzy submodules and fuzzy module homomorphisms.
Main Methods:
- Generalization of existing definitions from fuzzy group and fuzzy ring theories.
- Exploration of properties analogous to those in ordinary module theory.
Main Results:
- Definition of a new algebraic structure: fuzzy modules over fuzzy rings.
- Characterization of fuzzy submodules and fuzzy module homomorphisms.
- Demonstration of properties analogous to classical module theory.
Conclusions:
- The proposed fuzzy module structure provides a new framework within fuzzy algebra.
- The study establishes foundational properties for fuzzy submodules and homomorphisms.
- This work offers a basis for further research in generalized fuzzy algebraic structures.
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