  Endomorphism rings of modules appear as the center of a ring, as the fix ring
of ring with group action or as the subring of constants of a derivation. This
note discusses the question whether certain *-prime modules (introduced by
Bican et al.) have a prime endomorphism ring. Several conditions are presented
that guarantee the primness of the endomorphism ring. The contours of a
possible example of a *-prime module whose endomorphism ring is not prime are
traced.
