On the stable hom relation and stable degenerations of Cohen–Macaulay modules

Abstract We study the stable hom relation for Cohen–Macaulay modules over Gorenstein local algebras. We give the sufficient condition to make the stable hom relation a partial order when the base algebra is of finite representation type. As an application, we give the description of stable degenerations of Cohen–Macaulay modules over simple singularities of several types by using the stable hom relation.