EXTENDED CENTRES OF FINITELY GENERATED PRIME ALGEBRAS

Jason P. Bell, Agata Smoktunowicz

Research output: Contribution to journalArticlepeer-review

Abstract

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 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 algebraic over 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.

Original languageEnglish
Pages (from-to)332-345
Number of pages14
JournalCommunications in Algebra
Volume38
Issue number1
DOIs
Publication statusPublished - 13 Jan 2010

Keywords

  • Extended centre
  • GK dimension
  • Quadratic growth
  • Transcendence degree
  • GELFAND-KIRILLOV DIMENSION

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