The universality of Hughes-free division rings

Jaikin Zapirain, Andrés

UAM_Biblioteca

Author

Jaikin Zapirain, Andrés

Entity

UAM. Departamento de Matemáticas

Publisher

Springer

Date

2021-07-28

Citation

Selecta Mathematica (New Series) 27.4 (2021): 74

ISSN

1022-1824 (print); 1420-9020 (online)

DOI

10.1007/s00029-021-00691-w

Funded by

This paper is partially supported by the Spanish Ministry of Science and Innovation through the grant MTM2017-82690-P and the “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S4). I would like to thank Dawid Kielak and an anonymous referee for useful suggestions and comments

Project

Gobierno de España. MTM2017-82690-P

Editor's Version

https://doi.org/10.1007/s00029-021-00691-w

Subjects

Hughes-free division ring; Locally indicable groups; Universal division ring of fractions; Matemáticas

URI

http://hdl.handle.net/10486/700617

Rights

Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.

Abstract

Let E∗ G be a crossed product of a division ring E and a locally indicable group G. Hughes showed that up to E∗ G-isomorphism, there exists at most one Hughes-free division E∗G-ring. However, the existence of a Hughes-free division E∗ G-ring DE∗G for an arbitrary locally indicable group G is still an open question. Nevertheless, DE∗G exists, for example, if G is amenable or G is bi-orderable. In this paper we study, whether DE∗G is the universal division ring of fractions in some of these cases. In particular, we show that if G is a residually-(locally indicable and amenable) group, then there exists DE[G] and it is universal. In Appendix we give a description of DE[G] when G is a RFRS group

Show full item record