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Nil algebras with restricted growth

Part of: Chain conditions, growth conditions, and other forms of finiteness Radicals and radical properties of rings

Published online by Cambridge University Press:  23 February 2012

T. H. Lenagan ,
Agata Smoktunowicz  and
Alexander A. Young
T. H. Lenagan
Affiliation:
Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK ([email protected]; [email protected])
Agata Smoktunowicz
Affiliation:
Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK ([email protected]; [email protected])
Alexander A. Young
Affiliation:
Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA ([email protected])
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Abstract

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It is shown that over an arbitrary countable field there exists a finitely generated algebra that is nil, infinite dimensional and has Gelfand–Kirillov dimension at most 3.

Keywords

nil algebrasgrowth of algebrasGelfand–Kirillov dimension

MSC classification

Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings 16P90: Growth rate, Gelfand-Kirillov dimension
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 461 - 475
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

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