Israel Journal of Mathematics

, Volume 206, Issue 1, pp 313–325 | Cite as

Gelfand-Kirillov dimension of algebras with locally nilpotent derivations



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).


Polynomial Ring Prime Ring Polynomial Identity Nonzero Ideal Nilpotent Derivation 


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© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Department of MathematicsDePaul UniversityChicagoUSA
  2. 2.Faculty of Computer ScienceBiałystok University of TechnologyBiałystokPoland

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