On the arithmetic of Krull monoids with finite Davenport constant.
The authors study factorization properties of Krull monoids \(H\) (i.e. commutative cancellative semigroups with divisor theory) in which the set \(G_P\) of classes containing prime divisors has a finite Davenport constant. It has been known that if \(G_P\) is finite, then for \(h\in H\) the set of lengths of factorizations of \(h\) forms an almost arithmetical multiprogression having uniformly bounded length. The main result of the paper shows that the same holds under the weaker assumption of finiteness of Davenport's constant of \(G_P\). The central point of the long combinatorial proof is an assertion about factorization patterns in factorization monoids of Abelian groups (Proposition 4.3), providing a bound on the cardinality of tame generating sets for pattern ideals.
scientific article; zbMATH DE number 5549358
scientific article