On the Kurosh problem for algebras over a general field

Details On the Kurosh problem for algebras over a general field On the Kurosh problem for algebras over a general field

2011-02-02

arxiv.org/abs/1102.0362v1

Mathematics

Rings and Algebras

18 pages; comments welcome

Scientific paper

Smoktunowicz, Lenagan, and the second-named author recently gave an example of a nil algebra of Gelfand-Kirillov dimension at most three. 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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