2007/04/18 by Jason P. Bell, Bell, Jason P., Agata Smoktunowicz +1
Mathematics · #16P90 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16P90
paper · pdf · doi:10.48550/arxiv.0704.2378
17 pages
arxiv created 2007/04/18 · openalex publication_date 2007/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.