# The Class Group and Local Class Group of an Integral Domain

• David F. Anderson
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 520)

## Abstract

This article gives a survey of recent developments on the (t-)class group and local (t-)class group of an integral domain R. Let T (R) be the group of t-invertible (fractional) t-ideals of R under t-multiplication, and let Prin (R) (resp., Inv (R)) be its subgroup of principal (resp., invertible) (fractional) ideals. Then Cl (R) = T (R)/Prin (R) is an abelian group, called the (t-)class group of R; the Picard group of R is Pic (R) = Inv (R)/Prin (R); and the local (t-)class group of R is G (R) = T (R)/Inv (R) = Cl (R)/Pic (R). If R is a Krull domain, then Cl (R) is the usual divisor class group of R, and if R is a Prüfer domain, then Cl (R) (= Pic (R)) is just the ideal class group of R.

## Keywords

Class Group Integral Domain Valuation Domain Mori Domain Ideal Class Group
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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