The prime spectrum of algebras of quadratic growth
| dc.creator | Bell, Jason P. | |
| dc.creator | Smoktunowicz, Agata | |
| dc.date | 2007-04-18 | |
| dc.date.accessioned | 2026-07-07T07:57:04Z | |
| dc.date.available | 2026-07-07T07:57:04Z | |
| dc.description | We study prime algebras of quadratic growth. Our first result is that if $A$ is a prime monomial algebra of quadratic growth then $A$ has finitely many prime ideals $P$ such that $A/P$ has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the nonzero prime ideals $P$ such that $A/P$ has GK dimension 2 is non-empty, provided there is at least one such ideal. From this we conclude that a prime monomial algebra of quadratic growth is either primitive or has nonzero locally nilpotent Jacobson radical. Finally, we show that there exists a prime monomial algebra $A$ of GK dimension two with unbounded matrix images and thus the quadratic growth hypothesis is necessary to conclude that there are only finitely many prime ideals such that $A/P$ has GK dimension 1. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0704.2381 | |
| dc.identifier | http://arxiv.org/abs/0704.2381 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127547 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16P90 | |
| dc.title | The prime spectrum of algebras of quadratic growth | |
| dc.type | text |