Primitive algebraic algebras of polynomially bounded growth

Jason P. Bell, Lance W. Small, Agata Smoktunowicz

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.
Original languageEnglish
Title of host publicationNew Trends in Noncommutative Algebra
Subtitle of host publicationA Conference in Honor of Ken Goodearl’s 65th Birthday
Editors P Ara, K. A. Brown, T. H. Lenagan, E. S. Letzter, J. T. Stafford, J. J. Zhang
PublisherAmerican Mathematical Society
Number of pages12
ISBN (Electronic)978-0-8218-8497-3
ISBN (Print)978-0-8218-5297-2
Publication statusPublished - 2012


  • math.RA


Dive into the research topics of 'Primitive algebraic algebras of polynomially bounded growth'. Together they form a unique fingerprint.

Cite this