Affiliations: Department of Mathematics, Kookmin University, Seoul, Korea | Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea | Department of Mathematics, Hallym University, Chuncheon, Korea
Note: [] Corresponding author. Keum Sook So, Department of Mathematics, Hallym University, Chuncheon 200-702, Korea. Tel.: +82 33 248 2011; Fax: +82 33 256 2011; E-mail: ksso@hallym.ac.kr
Abstract: In this paper we introduce the notion of a fuzzy polynomial ideal αx 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 αx. It is shown that a fuzzy ideal α of a ring is fuzzy prime if and only if αx is a fuzzy prime ideal of R[x]. Moreover, we show that if αx is a fuzzy maximal ideal of R[x], then α is a fuzzy maximal ideal of R.
