Chains of factorizations and sets of lengths
In the theory of nonunique factorization in integral domains, a crucial invariant is the set of lengths of factorizations. If \(R\) is a Krull domain with finite divisor class group, then sets of lengths are almost arithmetical progressions. This paper investigates chains of factorizations and sets of lengths in the setting of weakly Krull monoids. The main result (for domains) is that for a Noetherian weakly Krull domain \(R\) with finite \(t\)-class group and whose integral closure is a finite \(R\)-module, there is a positive integer \(C\) such that for all nonzero nonunits \(a\) of \(R\) and each two factorizations \(z\) and \(z'\) of \(a\), there is a \(C\)-chain of factorizations from \(z\) to \(z'\) whose lengths form an almost arithmetical progression.
nonunique factorizations in integral domains
scientific article; zbMATH DE number 1013927
scientific article