Fuchs (Abelian groups, Pergamon, Oxford, 1960, Problem 72) asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs' question when A is a finite characteristic ring. The result is a pretty good description of the groups which can occur as group of units in this case, equipped with examples showing that there are obstacles to a "short" complete classification. As a by-product, we are able to classify all possible cardinalities of the group of units of a finite characteristic ring, so to answer Ditor's question (Ditor in Am Math Mon 78(5):522-523, 1971).
Finite groups of units of finite characteristic rings
Del Corso, Ilaria;Dvornicich, Roberto
2018-01-01
Abstract
Fuchs (Abelian groups, Pergamon, Oxford, 1960, Problem 72) asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs' question when A is a finite characteristic ring. The result is a pretty good description of the groups which can occur as group of units in this case, equipped with examples showing that there are obstacles to a "short" complete classification. As a by-product, we are able to classify all possible cardinalities of the group of units of a finite characteristic ring, so to answer Ditor's question (Ditor in Am Math Mon 78(5):522-523, 1971).File | Dimensione | Formato | |
---|---|---|---|
units_finiti.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
288.63 kB
Formato
Adobe PDF
|
288.63 kB | Adobe PDF | Visualizza/Apri |
AMPA.pdf
solo utenti autorizzati
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
398.54 kB
Formato
Adobe PDF
|
398.54 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.