Primitivity of finitely presented monomial algebras.

DOI10.1016/j.jpaa.2008.11.039zbMath1182.16017arXiv0712.0815OpenAlexW2031365917MaRDI QIDQ1013104

Jason P. Bell, Pinar Colak

Publication date: 16 April 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0815

zbMATH Keywords

prime algebrasmonomial algebrasPI algebrasfinitely presented algebrasprimitive algebrasautomaton algebras

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Growth rate, Gelfand-Kirillov dimension (16P90) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Related Items (11)

Gröbner bases for quadratic algebras of skew type ⋮ On the semiprimitivity of finitely generated algebras ⋮ Trichotomy for finitely generated monomial algebras. ⋮ Unions of chains of primes ⋮ Finitely presented monoids and algebras defined by permutation relations of Abelian type. ⋮ On a Class of Automaton Algebras ⋮ 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. ⋮ Finitely presented algebras defined by permutation relations of dihedral type ⋮ Gröbner basis and the automaton property of Hecke-Kiselman algebras

Cites Work

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• Prime affine algebras of Gelfand-Kirillov dimension one
• On the primitivity of prime rings
• Monomial algebras
• Algebras which are nearly finite dimensional and their identities
• Examples in finite Gel'fand-Kirillov dimension
• The prime spectrum of algebras of quadratic growth.
• Automatic Sequences
• A Ring Primitive on the Right But Not on the Left

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