Illinois Journal of Mathematics

Acyclicity over local rings with radical cube zero

Lars Winther Christensen and Oana Veliche

Full-text: Open access


This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring $(R,\fm)$ with $\fm^3=0$. 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 $\Ext{n}{R}{M}{R}=0$ for a few $n>0$.

Article information

Illinois J. Math., Volume 51, Number 4 (2007), 1439-1454.

First available in Project Euclid: 13 November 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D25


Christensen, Lars Winther; Veliche, Oana. Acyclicity over local rings with radical cube zero. Illinois J. Math. 51 (2007), no. 4, 1439--1454. doi:10.1215/ijm/1258138553.

Export citation