The prime spectrum of algebras of quadratic growth.

DOI10.1016/j.jalgebra.2007.08.026zbMath1136.16019arXiv0704.2381OpenAlexW2074063595MaRDI QIDQ2470409

Jason P. Bell, Agata Smoktunowicz

Publication date: 14 February 2008

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

Full work available at URL: https://arxiv.org/abs/0704.2381

zbMATH Keywords

graded algebrasGelfand-Kirillov dimensionprimitive ringsPI ringsBergman gap theoremnumbers of prime idealsprime monomial algebrasquadratic growth of algebras

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Growth rate, Gelfand-Kirillov dimension (16P90) Graded rings and modules (associative rings and algebras) (16W50) Ideals in associative algebras (16D25) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Jacobson radical, quasimultiplication (16N20)

Related Items (11)

Lie complexity of words ⋮ Topological invariants for words of linear factor complexity ⋮ Trichotomy for finitely generated monomial algebras. ⋮ Unions of chains of primes ⋮ Affine algebras with arbitrary simple modules ⋮ Structure of prime finitely presented monomial algebras. ⋮ Finitely presented algebras and groups defined by permutation relations. ⋮ A dichotomy result for prime algebras of Gelfand-Kirillov dimension two. ⋮ Iterative algebras. ⋮ Primitivity of finitely presented monomial algebras. ⋮ Chains of prime ideals and primitivity of \(\mathbb Z\)-graded algebras.

Cites Work

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• On radicals of monomial algebras
• Automatic Sequences
• The Semigroup of Ideals of a Fir is (Usually) Free
• Examples in Finite Gel'fand–Kirillov Dimension. II

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