On generalized lengths of factorizations in Dedekind and Krull domains. (Q2752905)

This paper is a review of recent results on the so-called half-factorial domains and its variations. As such it is closely related to another survey in the same volume [see \textit{S. T. Chapman} and \textit{J. Coykendall}, ``Half-factorial domains, a survey'', in: Non-Noetherian commutative ring theory, Math. Appl., Dordr. 520, 97-115 (2000; see the preceding review Zbl 0987.13010)]. The authors of the present paper develop or survey a few technical flexibilizations of the notion of a UFD in the realm of Dedekind and Krull domains, most of which have to do with the variation of the lengths in the decomposition into irreducibles. The reader will find it surprising how much of technical variation is yet available within such classical objects as number fields with non-zero class number. Of course the real test for such yearning is ultimately the mathematical depth such generalizations may attain.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00012].