Golod-Shafarevich algebras, free subalgebras and Noetherian images.

DOI10.1016/J.JALGEBRA.2013.02.003zbMath1302.16018arXiv1207.6503OpenAlexW2964048702MaRDI QIDQ375198

Agata Smoktunowicz

Publication date: 28 October 2013

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

Full work available at URL: https://arxiv.org/abs/1207.6503

zbMATH Keywords

nil algebrasfree algebrasfinitely presented algebrasNoetherian algebrasJacobson radical algebrasPI-algebrasalgebras of linear growthGolod-Shafarevich algebras

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Growth rate, Gelfand-Kirillov dimension (16P90) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Jacobson radical, quasimultiplication (16N20) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (3)

Free subalgebras of graded algebras ⋮ Optimal 5-step nilpotent quadratic algebras ⋮ Growth, entropy and commutativity of algebras satisfying prescribed relations.

Cites Work

• Prime affine algebras of Gelfand-Kirillov dimension one
• Golod-Shafarevich groups with property \((T)\) and Kac-Moody groups.
• Non-commutative graded algebras and their Hilbert series
• Finite dimensional semigroup quadratic algebras with the minimal number of relations
• Polynomial identity rings.
• Free subalgebras of division algebras over uncountable fields.
• Nil algebras with restricted growth
• Konstruktion nilpotenter assoziativer Algebren mit wenig Relationen
• An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
• Affine algebras of Gelfand-Kirillov dimension one are PI
• SOME OPEN PROBLEMS IN THE THEORY OF INFINITE DIMENSIONAL ALGEBRAS
• Some results on the center of a ring with polynomial identity
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