On the regularity over positively graded algebras

Details On the regularity over positively graded algebras On the regularity over positively graded algebras

2006-12-20

arxiv.org/abs/math/0612581v2

J. Algebra 319, No. 1, 1-15 (2008)

Mathematics

Commutative Algebra

13 pages; Revised version of the paper

Scientific paper

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 an 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.

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