Singular equivalences induced by ring extensions
Abstract
Let B ⊂eq 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.
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