Extended centres of finitely generated prime algebras

dc.creatorBell, Jason P.
dc.creatorSmoktunowicz, Agata
dc.date2007-04-18
dc.date.accessioned2026-07-07T07:57:04Z
dc.date.available2026-07-07T07:57:04Z
dc.descriptionLet $K$ 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.description17 pages
dc.identifierhttps://arxiv.org/abs/0704.2378
dc.identifierhttp://arxiv.org/abs/0704.2378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127546
dc.subjectRings and Algebras
dc.subject16P90
dc.titleExtended centres of finitely generated prime algebras
dc.typetext

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