Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584993 | Journal of Algebra | 2013 | 16 Pages |
Abstract
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t±1]-module associated to R. This module, denoted J(R), is the free Z[t±1]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The main result is a structure theorem for J(R) when R is a complete Gorenstein local ring; the link between periodicity and torsion stated above is a corollary.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Amanda Croll,