On self-orthogonal modules in Iwanaga–Gorenstein rings

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.