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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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>kernels</mi></semantics></math></inline-formula> 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.