Integral domains with finitely generated groups of divisibility

D.D. Anderson

doi:10.1090/S0002-9939-1991-1055765-X

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Integral domains with finitely generated groups of divisibility

Journal article

Open access

Peer reviewed

Integral domains with finitely generated groups of divisibility

D.D. Anderson

Proceedings of the American Mathematical Society, Vol.112, pp.613-618

1991

DOI: 10.1090/S0002-9939-1991-1055765-X

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Abstract

Let D be an integral domain with integral closure D. We show that the group ofdivisibility G(D) of D is finitely generated if and only if G(D) is finitely generated and D/[D: D] is finite. We also show that G(D) is finitely generated if and only if the monoid of finitely generated fractional ideals of D (under multiplication) is finitely generated. © 1991 American Mathematical Society.

Details

Title: Subtitle: Integral domains with finitely generated groups of divisibility
Creators: D.D. Anderson
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.112, pp.613-618
DOI: 10.1090/S0002-9939-1991-1055765-X
ISSN: 0002-9939
Language: English
Date published: 1991
Academic Unit: Mathematics
Record Identifier: 9984230628802771

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