A fuzzy version of uniformly strongly prime ideals

This paper is a step forward in the field of fuzzy algebra. Its main target is the investigation of some properties about uniformly strongly prime fuzzy ideals (USPf) based on a definition without a-cuts dependence. This approach is relevant because it is possible to find pure fuzzy results and to see clearly how the fuzzy algebra is different from classical algebra. For example: in classical ring theory an ideal is uniformly strongly prime (USP) if and only if its quotient is a USP ring, but as we shall demonstrate here, this statement does not happen in the fuzzy algebra. Also, we investigate the Zadeh's extension on USPf ideals.