A dichotomy result for prime algebras of Gelfand-Kirillov dimension two.

DOI10.1016/j.jalgebra.2010.03.028zbMath1216.16010arXiv0911.4214OpenAlexW1994112470MaRDI QIDQ994287

Jason P. Bell

Publication date: 17 September 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.4214

zbMATH Keywords

domainsNoetherian ringsquadratic growthprimitive ringsPI ringsGK dimension

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) Noetherian rings and modules (associative rings and algebras) (16P40) Identities other than those of matrices over commutative rings (16R40) Integral domains (associative rings and algebras) (16U10)

Related Items (3)

Lie complexity of words ⋮ On the stability of waves of nonlinear parabolic systems ⋮ Chains of prime ideals and primitivity of \(\mathbb Z\)-graded algebras.

Cites Work

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• Examples in finite Gel'fand-Kirillov dimension
• Noncommutative graded domains with quadratic growth
• The prime spectrum of algebras of quadratic growth.
• There are no graded domains with GK dimension strictly between 2 and 3.
• Centers in domains with quadratic growth.
• The Goldie conditions for Algebras with Bounded Growth
• Affine algebras of Gelfand-Kirillov dimension one are PI
• Examples in Finite Gel'fand–Kirillov Dimension. II

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