Abstract: Let R be an artin algebra. In his Philadelphia Notes (published in 1978), Auslander showed that any homomorphism between R-modules is right determined by an R-module. This topic is also the theme of the last chapter in the book of Auslander, Reiten and Smalo. But it seems that the relevance of these considerations has not yet found the attention they deserve.
One reason seems to be the somewhat misleading terminology, this will be discussed in the first lecture where we outline a direct approach. We will draw the attention to the indecomposable direct summands of the minimal right determiner of a morphism. In paricular the role of its projective direct summands is of great interest.
The second lecture will provide a detailed analysis of those morphisms which are right determined by a module without any non-zero projective direct summand. Here we encounter an intimate relationship to the vanishing of Ext^2.