论文信息 - Unions of sets of lengths

Unions of sets of lengths

Let H be a Krull monoid such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number elds). For k 2 N let Vk(H) denote the set of all m 2 N with the following property : There exist atoms (irreducible elements) u1; : : : ; uk; v1; : : : ; vm 2 H with u1 : : : uk = v1 : : : vm. We show that the sets Vk(H) are intervals for all k 2 N. This solves Problem 37 in [4]. Dedicated to Professor W. Narkiewicz on the occasion of his seventieth birthday

Alfred Geroldinger | Michael Freeze

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