Golod-Shafarevich algebras, free subalgebras and Noetherian images

TL;DR

This paper demonstrates that Golod-Shafarevich algebras with few relations contain free subalgebras, can map onto Noetherian algebras with linear growth, and are not nil, advancing understanding of their structure.

Contribution

It establishes the existence of free subalgebras and homomorphic images in Golod-Shafarevich algebras with few relations, revealing new structural properties.

Findings

Golod-Shafarevich algebras contain free subalgebras in two generators

Such algebras can be mapped onto prime, Noetherian algebras with linear growth

They cannot be nil under reduced relations

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.