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Journal of the London Mathematical Society 1998 57(2):336-350; doi:10.1112/S0024610798006164
© 1998 by London Mathematical Society
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© The London Mathematical Society

Non-Commutative Graded Homological Identities

Peter Jørgensen

Matematisk Afdeling, Københavns Universitet Universitetsparken 5, DK-2100 København Ø, Denmark. E-mail: popjoerg{at}math.ku.dk

Received 3 August 1995. Revision received 29 March 1996.

Two results, the Auslander–Buchsbaum and Bass Theorems from the homological theory of commutative noetherian rings, are generalized to important classes of non-commutative N-graded algebras over fields. As a corollary to the generalized Auslander–Buchsbaum Theorem, it is found that under weak (so-called {chi}–) conditions, a non-commutative N-graded connected noetherian algebra of finite global dimension is in fact Artin–Schelter regular.


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