Acyclicity over local rings with radical cube zero

Abstract

This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring (R, m) with m3 = 0. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient conditions are given for total acyclicity. Results are also obtained on the structure of rings that are not Gorenstein and admit acyclic complexes; part of this structure is exhibited by every ring R that admits a non-free finitely generated module M with Extn R(M, R) = 0 for a few n > 0. ©2007 University of Illinois.

Description

None

Keywords

Betti numbers, Complete resolutions, Infinite syzygies, Infinite syzygy, Minimal free resolutions, Totally acyclic complexes, Totally reflexive modules

Citation

Christensen, L.W., & Veliche, O.. 2008. Acyclicity over local rings with radical cube zero. Illinois Journal of Mathematics, 51(4). https://doi.org/10.1215/ijm/1258138553

Collections