Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584706 | Journal of Algebra | 2014 | 12 Pages |
Abstract
A module of complexity c for E≅(Z/p)rE≅(Z/p)r in characteristic p has Loewy length at least (p−1)(r−c)+1(p−1)(r−c)+1. We study the case of equality. If p is odd, the only rank varieties possible are finite unions of linear subspaces of dimension c , and every such rank variety occurs. If p=2p=2, the variety has to be equidimensional. If such a variety is a finite union of set theoretic complete intersections then it occurs for such a module, but otherwise the situation is unclear. Exterior algebras in any characteristic are also treated, and follow the same behaviour as the case p=2p=2 above.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dave Benson, Fergus Reid,