Singular equivalences induced by ring extensions

Abstract

Let $B\subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result is applied to trivial extensions, Morita rings and triangular matrix algebras to give several reduction methods on singularity categories and Gorenstein defect categories of algebras.