Radical Structures of Fuzzy Polynomial Ideals in a Ring

الملخص EN

We investigate the radical structure of a fuzzy polynomial ideal induced by a fuzzy ideal of a ring and study its properties.

Given a fuzzy ideal β of R and a homomorphism f : R → R ′ , we show that if f x is the induced homomorphism of f , that is, f x ( ∑ i = 0 n a i x i ) = ∑ i = 0 n f ( a i ) x i , then f x - 1 [ ( β ) x ] = ( f - 1 ( β ) ) x .