Acyclic Complexes and Graded Algebras

Chaoyuan Zhou ()
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Chaoyuan Zhou: School of Science, Shanghai University, Shanghai 200444, China

Mathematics, 2023, vol. 11, issue 14, 1-22

Abstract: We already know that the noncommutative N -graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated graded free modules is totally acyclic, and we want to generalize such properties to noncommutative N -graded Noetherian algebra. By generalizing the conclusions about commutative rings and combining what we already know about noncommutative graded algebras, we identify a class of noncommutative graded algebras with the property that every minimal acyclic complex of finitely generated graded free modules is totally acyclic. We also discuss how the relationship between AS–Gorenstein algebras and AS–Cohen–Macaulay algebras admits a balanced dualizing complex. We show that AS–Gorenstein algebras and AS–Cohen–Macaulay algebras with a balanced dualizing complex belong to this algebra.

Keywords: AS–Gorenstein algebra; AS–Cohen–Macaulay algebra; acyclic complex; totally acyclic complex; balanced dualizing complex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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