  One of the most stunning results in the representation theory of
Cohen-Macaulay rings is Auslander's well known theorem which states a CM local
ring of finite CM type can have at most an isolated singularity. There have
been some generalizations of this in the direction of countable CM type by
Huneke and Leuschke. In this paper, we focus on a different generalization by
restricting the class of modules. Here we consider modules which are high
syzygies of MCM modules over non-commutative rings, exploiting the fact that
non-commutative rings allow for finer homological behavior. We then generalize
Auslander's Theorem in the setting of complete Gorenstein local domains by
examining path algebras, which preserve finiteness of global dimension.
