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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