Integral domains with finitely generated groups of divisibility

D. D. Anderson
1991 Proceedings of the American Mathematical Society  
Let D be an integral domain with integral closure D. We show that the group of divisibility 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.
doi:10.1090/s0002-9939-1991-1055765-x fatcat:b6jkfmgztfgkrfqoyll6xivhw4