Golod-Shafarevich algebras, free subalgebras and Noetherian images

2012/07/27 by Smoktunowicz, Agata
#16 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1207.6503

Abstract

It is shown that Golod-Shaferevich algebras of a reduced number of defining relations contain noncommutative free subalgebras in two generators, and that these algebras can be homomorphically mapped onto prime, Noetherian algebras with linear growth. It is also shown that Golod-Shafarevich algebras of a reduced number of relations cannot be nil.

Related

• Growth, entropy and commutativity of algebras satisfying prescribed relations
• A remark on Golod--Shafarevich algebras
• The Golod Shafarevich counter-example without Hilbert series
• Makar-Limanov's conjecture on free subalgebras
• Golod-Shafarevich-Vinberg type theorems and finiteness conditions for potential algebras