chapter  14
20 Pages

On Inside Factorial Integral Domains

ByDavid E. Dobbs, Gabriel Picavet, and Martine Picavet-L’Hermitte

Let us first collect some notation. If R is a (commutative) integral domain, we let R× denote the multiplicative monoid R \ {0}; U(R) the set of units of R; R′ the integral closure of R (in its quotient field); Spec(R) the set of prime ideals of R; Max(R) the set of maximal ideals of R; X(1)(R) the set of height 1 prime ideals of


R; dim(R) the (Krull) dimension of R; Clt(R) the t-class group of R (in the sense of [1]); and Pic(R) the Picard group of R. It is also convenient to let N (resp., N0) denote the set of positive (resp., nonnegative) integers.