  Let $A$ be an Iwanaga-Gorenstein ring. Enomoto conjectured that a
self-orthogonal $A$-module has finite projective dimension. We prove this
conjecture for $A$ having the property that every indecomposable non-projective
maximal Cohen-Macaulay module is periodic. This answers a question of Enomoto
and shows the conjecture for monomial quiver algebras and hypersurface rings.
