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A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let Dk(G) denote the smallest ℓ such that each sequence over G of length at least ℓ has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (Dk(G))k∈N is eventually...
By a result of G. Freiman and A. Geroldinger [G. Freiman, A. Geroldinger, An addition theorem and its arithmetical application, J. Number Theory 85 (1) (2000) 59–73] it is known that the set of lengths of factorizations of an algebraic integer (in the ring of integers of an algebraic number field), or more generally of an element of a Krull monoid with finite class group, has a certain structure:...
Let H be a Krull monoid with finite class group such that each class contains a prime divisor (e.g., the multiplicative monoid of the ring of algebraic integers of some number field). It is shown that it can be determined whether the class group is of the form ℤ/nℤ⊕ℤ/nℤ, for n≥3, just by considering the system of sets of lengths of H.
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