Krull domains and monoids, their sets of lengths, and associated combinatorial problems. (English) Zbl 0897.13001

Chapman, Scott; Geroldinger, Alfred

Anderson, Daniel D. (ed.), Factorization in integral domains. Based on the proceedings of the conference, March 21, 1996, and the special session in commutative ring theory, March 22–23, 1996, at the 909th meeting of the American Mathematical Society, Iowa City, IA, USA. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 189, 73-112 (1997).

This paper is a survey on the theory of non-unique factorization concerning factorizations in Krull domains with finite divisor class group but restricting the interest to sets of lengths and the invariants derived from them. The language used in the paper is the one of monoids. So after discussing sets of lengths for Krull monoids in section 2, section 3 is devoted to study block monoids which allow to reduce ring theoretical problems to problems in finitely generated monoids. Finally some analytical aspects of non-unique factorization are summarized in section 4.
For the entire collection see [Zbl 0865.00039].

Reviewer: C.Galindo (Castellon)

MSC:

13A05	Divisibility and factorizations in commutative rings
13F15	Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
13G05	Integral domains
11R27	Units and factorization
13F05	Dedekind, Prüfer, Krull and Mori rings and their generalizations
20M05	Free semigroups, generators and relations, word problems
20M14	Commutative semigroups

Keywords:

factorization in Krull domains; length of Krull monoids; block monoids; non-unique factorization; finitely generated monoids