On the regularity over positively graded algebras

JOURNAL OF ALGEBRA

卷:319

Article

Roemer, Tim

关键词: regularity;    positively graded algebras;    Koszul algebras;    linear resolutions;    local cohomology;    free resolutions;   

DOI  :  10.1016/j.jalgebra.2007.08.031

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free