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 = 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.

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