On the regularity over positively graded algebras

Autor(en): Roemer, Tim 
Stichwörter: free resolutions; KOSZUL ALGEBRAS; LINEAR FREE RESOLUTIONS; linear resolutions; local cohomology; Mathematics; positively graded algebras; regularity
Erscheinungsdatum: 2008
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF ALGEBRA
Volumen: 319
Ausgabe: 1
Startseite: 1
Seitenende: 15
Zusammenfassung: 
We study the relationship between the Tor-regularity and the local-regularity over a positively graded algebra defined over a field which coincide if the algebra is a standard graded polynomial ring. In this case both are characterizations of the so-called Castelnuovo-Mumford regularity. Moreover, we can characterize a standard graded polynomial ring as a K-algebra with extremal properties with respect to the Tor- and the local-regularity. For modules of finite projective dimension we get a nice formula relating the two regularity notions. Interesting examples are given to help to understand the relationship between the Tor- and the local-regularity in general. (C) 2007 Elsevier Inc. All rights reserved.
ISSN: 00218693
DOI: 10.1016/j.jalgebra.2007.08.031

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