Extended centres of finitely generated prime algebras
| 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 | Let $K$ be a field and let $A$ be a finitely generated prime $K$-algebra. We generalize a result of Smith and Zhang, showing that if $A$ is not PI and does not have a locally nilpotent ideal, then the extended centre of $A$ has transcendence degree at most ${\rm GKdim}(A)-2$ over $K$. As a consequence, we are able to show that if $A$ is a prime $K$-algebra of quadratic growth, then either the extended centre is a finite extension of K or $A$ is PI. Finally, we give an example of a finitely generated non-PI prime $K$-algebra of GK dimension 2 with a locally nilpotent ideal such that the extended centre has infinite transcendence degree over $K$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0704.2378 | |
| dc.identifier | http://arxiv.org/abs/0704.2378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127546 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16P90 | |
| dc.title | Extended centres of finitely generated prime algebras | |
| dc.type | text |