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Ideals and Homomorphism Theorems of Fuzzy Associative Algebras

Author

Listed:
  • Xiaoman Yang

    (School of Mathematics and Statistics, Yili Normal University, Yining 835000, China)

  • Xin Zhou

    (School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
    Institute of Applied Mathematics, Yili Normal University, Yining 835000, China)

Abstract

Based on the definitions of fuzzy associative algebras and fuzzy ideals, it is proven that the intersections of fuzzy subalgebras are fuzzy subalgebras, and the intersections of fuzzy ideals are fuzzy ideals. Moreover, we prove that the kernels of fuzzy homomorphisms are fuzzy ideals. Using fuzzy ideals, the quotient structures of fuzzy associative algebras are constructed, their corresponding properties are discussed, and their homomorphism theorems are proven.

Suggested Citation

  • Xiaoman Yang & Xin Zhou, 2024. "Ideals and Homomorphism Theorems of Fuzzy Associative Algebras," Mathematics, MDPI, vol. 12(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1125-:d:1372567
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