Free groups in a normal subgroup of the field of fractions of a skew polynomial ring

Autor(es)

Goncalves, Jairo Z.

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 45, n. 12, p. 5193-5201, 2017.
• Citações Web of Science: 1

Resumo

Let k(t) be the field of rational functions over the field k, let sigma be a k-automorphism of K=k(t), let D=K(X;sigma) be the ring of fractions of the skew polynomial ring K{[}X;sigma], and let D-. be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D-., then N contains a free subgroup. We also prove that when k is algebraically closed and sigma has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D-.. (AU)

• Processo FAPESP: 15/09162-9 - Álgebra não comutativa e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático