Abstract In 1960, Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper, we address Fuchs' question for finitely generated abelian groups and consider the problem of characterizing those groups which arise in some fixed classes of rings C, namely, the integral domains, the torsion free rings and the reduced rings. Most of the paper is devoted to the study of the class of torsion-free rings, which needs a substantially deeper study.

Finitely generated abelian groups of units

Del Corso, Ilaria
Primo
2020-01-01

Abstract

Abstract In 1960, Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper, we address Fuchs' question for finitely generated abelian groups and consider the problem of characterizing those groups which arise in some fixed classes of rings C, namely, the integral domains, the torsion free rings and the reduced rings. Most of the paper is devoted to the study of the class of torsion-free rings, which needs a substantially deeper study.
2020
Del Corso, Ilaria
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1002521
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact