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Ext vanishing and infinite Auslander-Buchsbaum

Author(s): Peter Jørgensen
Journal: Proc. Amer. Math. Soc. 133 (2005), 1335-1341.
MSC (2000): Primary 16E30, 16W50
Posted: December 6, 2004
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Abstract: A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an ``infinite'' version is proved of the non-commutative Auslander-Buchsbaum theorem.

References:

1.: A. Frankild, Vanishing of local homology, Math. Z. 244 (2003), 615-630. MR 1992028 (2004d:13027)
2.: P. Jørgensen, Gorenstein homomorphisms of non-commutative rings, J. Algebra 211 (1999), 240-267. MR 1656580 (2000c:16013)
3.: -, Non-commutative graded homological identities, J. London Math. Soc. (2) 57 (1998), 336-350. MR 1644217 (99h:16010)
4.: J. J. Rotman, ``An Introduction to Homological Algebra'', Pure and Applied Mathematics, Vol. 85, Academic Press, New York, 1979. MR 0538169 (80k:18001)

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Additional Information:

Peter Jørgensen
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Email: popjoerg@maths.leeds.ac.uk

DOI: 10.1090/S0002-9939-04-07691-9
PII: S 0002-9939(04)07691-9
Keywords: $k$-flat dimension, depth, infinite non-commutative Auslander-Buchsbaum theorem, Ext groups, vanishing theorem
Received by editor(s): June 10, 2003
Received by editor(s) in revised form: February 2, 2004
Posted: December 6, 2004
Communicated by: Martin Lorenz
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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