ABSTRACT
This chapter recalls the properties of weakly Krull domains for the study of their arithmetic. Krull domains and noetherian domains, for which every prime ideal of depth one has height one, are weakly Krull. In the theory of non-unique factorizations, mainly sets of lengths, and associated invariants as the elasticity, are used to describe the arithmetic of a non-factorial domain. In Krull domains with finite divisor class group where each class contains prime divisor sets of lengths carry a great part of arithmetical information. The chapter discusses invariants as the catenary degree and the tame degree, which control the non-uniqueness of factorizations in a direct way. It derives explicit lower and upper bounds for the catenary and the tame degree in the case of Krull domains with finite class group where each class contains a prime divisor. The chapter also proves that in certain weakly Krull domains sets of lengths of large elements are arithmetical progressions with distance 1.
