On the fuzzy polynomial ideals

Abstract

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