On zero-sum sequences in .
Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörper.
Über nicht-eindeutige Zerlegungen in irreduzible Elemente.
Chains of factorizations in weakly Krull domains
A structure theorem for sets of lengths
Chains of factorizations in orders of global fields
On the structure and arithmetic of finitely primary monoids
Analytic and arithmetic theory of semigroups with divisor theory
The set of minimal distances in Krull monoids
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...
Zero-sumfree sequences in cyclic groups and some arithmetical application
We show that in a cyclic group with elements every zero-sumfree sequence with length contains some element of order with high multiplicity.
Congruence monoids
Non-unique factorizations in block semigroups and arithmetical applications
Inverse zero-sum problems {III}
Inverse zero-sum problems
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids
Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.
The catenary degree of Krull monoids I
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in an algebraic function field). The catenary degree of is the smallest integer with the following property: for each and each two factorizations of , there exist factorizations of such that, for each , arises from by replacing at most atoms from by at most new atoms. Under a very mild condition...
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