Krull Dimension for Differential Graded Algebras
Commutative Algebra
2013-06-03 v2
Abstract
We introduce a naive notion of a system of parameters for a homologically finite complex over a commutative noetherian local ring, and compare it to the system of parameters defined by Christensen. We show that these notions differ in general, but that they agree when the complex in question is a DG R-algebra. In this case we also show that the Krull dimension defined in terms of the lengths of such systems of parameters agrees with Krull dimensions defined in terms of certain chains of prime ideals.
Keywords
Cite
@article{arxiv.1210.7270,
title = {Krull Dimension for Differential Graded Algebras},
author = {Kristen A. Beck and Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:1210.7270},
year = {2013}
}
Comments
8 pages, v.2 has minor editorial changes. to appear in Arch. Math. (Basel)