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On the Kurosh problem for algebras of polynomial growth over a general field

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
342
Issue
1
Identifiers
DOI: 10.1016/j.jalgebra.2011.06.005
Keywords
  • KuroshʼS Problem
  • Nil Algebras
  • Algebraic Algebras
  • Growth
  • Subexponential Growth
Disciplines
  • Mathematics

Abstract

Abstract Lenagan and Smoktunowicz (2007) [LS] (see also Lenagan, Smoktunowicz and Young (in press) [LSY]) gave an example of a nil algebra of finite Gelfand–Kirillov dimension. Their construction requires a countable base field, however. We show that for any field k and any monotonically increasing function f ( n ) which grows super-polynomially but subexponentially there exists an infinite-dimensional finitely generated nil k-algebra whose growth is asymptotically bounded by f ( n ) . This construction gives the first examples of nil algebras of subexponential growth over uncountable fields.

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