  In this paper we introduce prime fuzzy ideals over a noncommutative ring.
This notion of primeness is equivalent to level cuts being crisp prime ideals.
It also generalizes the one provided by Kumbhojkar and Bapat in [Not-so-fuzzy
fuzzy ideals, Fuzzy Sets and Systems 37 (1990), 237--243], which lacks this
equivalence in a noncommutative setting. Semiprime fuzzy ideals over a
noncommutative ring are also defined and characterized as intersection of
primes. This allows us to introduce the fuzzy prime radical and contribute to
establish the basis of a Fuzzy Noncommutative Ring Theory.
