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.
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