## Illinois Journal of Mathematics

### 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 $(R,\fm)$ 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

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

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138553

Digital Object Identifier
doi:10.1215/ijm/1258138553

Mathematical Reviews number (MathSciNet)
MR2417436

Zentralblatt MATH identifier
1148.13008

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

#### Citation

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. https://projecteuclid.org/euclid.ijm/1258138553