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Abstract
We study prime algebras of quadratic growth. Our first result is that if A is a prime monomial algebra of quadratic growth then A has finitely many prime ideals P such that A/P has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the nonzero prime ideals P such that A I P has GK dimension 2 is nonzero, provided there is at least one such ideal. From this we conclude that a prime monomial algebra of quadratic growth is either primitive or has nonzero locally nilpotent Jacobson radical. Finally, we show that there exists a prime monomial algebra A of GK dimension two with unbounded matrix images and thus the quadratic growth hypothesis is necessary to conclude that there are only finitely many prime ideals such that A/P has GK dimension 1. (C) 2007 Elsevier Inc. All rights reserved.
Original language  English 

Pages (fromto)  414431 
Number of pages  18 
Journal  Journal of Algebra 
Volume  319 
Issue number  1 
DOIs  
Publication status  Published  1 Jan 2008 
Keywords
 GK dimension
 quadratic growth
 primitive rings
 PI rings
 graded algebra
 GELFANDKIRILLOV DIMENSION
 AFFINE ALGEBRAS
 EXAMPLES
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Dive into the research topics of 'The prime spectrum of algebras of quadratic growth'. 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