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Abstract
Let K be a field and let A be a finitely generated prime Kalgebra. 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 Kalgebra 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 nonPI prime Kalgebra of GK dimension 2 with a locally nilpotent ideal such that the extended centre has infinite transcendence degree over K.
Original language  English 

Pages (fromto)  332345 
Number of pages  14 
Journal  Communications in Algebra 
Volume  38 
Issue number  1 
DOIs  
Publication status  Published  13 Jan 2010 
Keywords
 Extended centre
 GK dimension
 Quadratic growth
 Transcendence degree
 GELFANDKIRILLOV DIMENSION
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Dive into the research topics of 'EXTENDED CENTRES OF FINITELY GENERATED PRIME ALGEBRAS'. Together they form a unique fingerprint.Projects
 1 Finished

Nil algebras, algebraic algebras and algebras with finite GelfandKirillov dimension
1/08/06 → 31/07/11
Project: Research