Zero-nonzero patterns for nilpotent matrices over finite fields
| dc.creator | Meulen, Kevin N. Vander | |
| dc.creator | Van Tuyl, Adam | |
| dc.date | 2008-12-02 | |
| dc.date.accessioned | 2026-07-07T12:08:39Z | |
| dc.date.available | 2026-07-07T12:08:39Z | |
| dc.description | Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper we initiate an investigation into which zero-nonzero patterns are potentially nilpotent over F, with a special emphasis on the case that F = Z_p is a finite field. As part of this investigation, we develop methods, using the tools of algebraic geometry and commutative algebra, to eliminate zero-nonzero patterns A as being potentially nilpotent over any field F. We then use these techniques to classify all irreducible zero-nonzero patterns of order two and three that are potentially nilpotent over Z_p for each prime p. | |
| dc.description | 16 Pages | |
| dc.identifier | https://arxiv.org/abs/0812.0527 | |
| dc.identifier | http://arxiv.org/abs/0812.0527 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209393 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | {15A18, 13P10 | |
| dc.title | Zero-nonzero patterns for nilpotent matrices over finite fields | |
| dc.type | text |