The prime spectrum of algebras of quadratic growth

Jason P. Bell, Agata Smoktunowicz

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 non-zero prime ideals P such that A I P has GK dimension 2 is non-zero, 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 non-zero 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 languageEnglish
Pages (from-to)414-431
Number of pages18
JournalJournal of Algebra
Volume319
Issue number1
DOIs
Publication statusPublished - 1 Jan 2008

Keywords / Materials (for Non-textual outputs)

  • GK dimension
  • quadratic growth
  • primitive rings
  • PI rings
  • graded algebra
  • GELFAND-KIRILLOV DIMENSION
  • AFFINE ALGEBRAS
  • EXAMPLES

Fingerprint

Dive into the research topics of 'The prime spectrum of algebras of quadratic growth'. Together they form a unique fingerprint.

Cite this