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]).