Reduction techniques of singular equivalences

DOI10.1016/J.JALGEBRA.2022.08.033arXiv2103.10393MaRDI QIDQ6363183

Publication date: 18 March 2021

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.

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Syzygies, resolutions, complexes in associative algebras (16E05) Derived categories and associative algebras (16E35)

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