On the fuzzy polynomial ideals

In this paper we introduce the notion of a fuzzy polynomial ideal alpha(x) of a polynomial ring R[x] induced by a fuzzy ideal alpha of a ring R, and obtain an isomorphism theorem of a ring of fuzzy cosets of alpha(x). It is shown that a fuzzy ideal alpha of a ring is fuzzy prime if and only if alpha(x) is a fuzzy prime ideal of R[x]. Moreover, we show that if alpha(x) is a fuzzy maximal ideal of R[x], then alpha is a fuzzy maximal ideal of R.