Gelfand-Kirillov dimension of algebras with locally nilpotent derivations |
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Authors: | Email author" target="_blank">Jeffrey?BergenEmail author Piotr?Grzeszczuk |
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Institution: | 1.Department of Mathematics,DePaul University,Chicago,USA;2.Faculty of Computer Science,Bia?ystok University of Technology,Bia?ystok,Poland |
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Abstract: | Let R be a finitely generated algebra over a field of characteristic 0 with a locally nilpotent derivation δ ≠ 0. We show that if {ie313-1}, where the invariants {ie313-2} are prime and satisfy a polynomial identity, then {ie313-3}. Furthermore, when R is a domain, the same conclusion holds without the assumption that R is finitely generated. This enables us to obtain a result on skew polynomial rings. These results extend work of Bell and Smoktunowicz on domains with GK dimension in the interval 2, 3). |
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