chapter  5
15 Pages

## Monotone Chains of Factorizations in C-Monoids

ByAndreas Foroutan, Alfred Geroldinger

C-monoids were recently introduced by F. Halter-Koch as a common generalization of various types of auxiliary monoids studied in factorization theory. C-monoids are suitably deﬁned submonoids of factorial monoids (cf. Deﬁnition 2.1), and they include Krull monoids with ﬁnite class groups and congruence monoids in Krull domains satisfying some natural ﬁniteness conditions. In particular, let A be a noetherian domain, R its integral closure and f = AnnA(R/A) = {0}. Then the multiplicative monoid A• of A is a congruence monoid in R, and if the class group C(R) and R/f are ﬁnite, then A• is a C-monoid ([12, Theorem 3.2] and [9, Corollary 6.4]).