  We deal with finitely generated modules over an artin algebra. In his
Philadelphia Notes, M.Auslander showed that any homomorphism is right
determined by a module C, but a formula for C which he wrote down has to be
modified. The paper includes now complete and direct proofs of the main results
concerning right determiners of morphisms. We discuss the role of
indecomposable projective direct summands of a minimal right determiner and
provide a detailed analysis of those morphisms which are right determined by a
module without any non-zero projective direct summand.
