#### Vol. 6, No. 1, 2014

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Local rings of embedding codepth $3$: A classification algorithm

### Lars Winther Christensen and Oana Veliche

Vol. 6 (2014), 1–8
##### Abstract

Let $I$ be an ideal of a regular local ring $Q$ with residue field $k$. The length of the minimal free resolution of $R=Q∕I$ is called the codepth of $R$. If it is at most $3$, then the resolution carries the structure of a differential graded algebra, and the induced algebra structure on ${Tor}_{\ast }^{Q}\left(R,k\right)$ provides for a classification of such local rings.

We describe the Macaulay2 package CodepthThree that implements an algorithm for classifying a local ring as above by computation of a few cohomological invariants.

##### Keywords
local ring, Tor algebra
##### Mathematical Subject Classification 2010
Primary: 13P20
Secondary: 13D02, 13H10
##### Supplementary material

CodepthThree source code

##### Milestones
Received: 16 February 2014
Revised: 11 July 2014
Accepted: 11 July 2014
Published: 2 October 2014
##### Authors
 Lars Winther Christensen Department of Mathematics and Statistics Texas Tech University Lubbock, TX 79409 United States Oana Veliche Department of Mathematics Northeastern University Boston, MA 02115 United States