Fuzzy homomorphism theorems on rings

Addis G. M., KAUSAR N., Munir M.

Journal of Discrete Mathematical Sciences and Cryptography, vol.25, no.6, pp.1757-1776, 2022 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1080/09720529.2020.1809777
  • Journal Name: Journal of Discrete Mathematical Sciences and Cryptography
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1757-1776
  • Keywords: 03E72, 05C60, 08A72, Fuzzy homomorphisms, Fuzzy ideals, Fuzzy isomorphism theorems, Fuzzy mappings, Quotient rings induced by fuzzy ideals
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we introduce the notion of fuzzy kernel of a fuzzy homomorphism on rings and show that it is a fuzzy ideal of the domain ring. Conversely, we also prove that any fuzzy ideal of a ring is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fundamental theorem of fuzzy homomorphism and the first, the second and the third fuzzy isomorphism theorems on rings.