Reduction techniques of singular equivalences (2103.10393v1)

Abstract: It is shown that a singular equivalence induced by tensoring with a suitable complex of bimodules defines a singular equivalence of Morita type with level, in the sense of Wang. This result is applied to homological ideals and idempotents to produce new reduction techniques for testing the properties of syzygy-finite and injectives generation of finite dimensional algebras over a field.