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

Let I be an ideal of a regular local ring Q with residue field k. The length of the minimal free resolution of R = QI 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 TorQ(R,k) 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.

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

CodepthThree source code

Received: 16 February 2014
Revised: 11 July 2014
Accepted: 11 July 2014
Published: 2 October 2014
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