  The aim of this paper is threefold: first, to prove that the endomorphism
ring associated to a pure subring of a regular local ring is a noncommutative
crepant resolution if it is maximal Cohen-Macaulay; second, to see that in that
situation, a different, but Morita equivalent, noncommutative crepant
resolution can be constructed by using Frobenius morphisms; finally, to study
the relation between Frobenius morphisms of noncommutative rings and the
finiteness of global dimension. As a byproduct, we will obtain a result on wild
quotient singularities: If the smooth cover of a wild quotient singularity is
unramified in codimension one, then the singularity is not strongly F-regular.
