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- W2080496329 abstract "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 fields). For $k in mathbb{N}$ let $mathcal{V}_k (H)$ denote the set of all $m in mathbb{N}$ with the following property{rm ,:} There exist atoms (irreducible elements) $u_1, ldots, u_k, v_1, ldots, v_m in H$ with $u_1 cdot ldots cdot u_k = v_1 cdot ldots cdot v_m$. We show that the sets $mathcal{V}_k (H)$ are intervals for all $k in mathbb{N}$. This solves Problem 37 in [4]." @default.
- W2080496329 created "2016-06-24" @default.
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- W2080496329 date "2008-11-01" @default.
- W2080496329 modified "2023-09-23" @default.
- W2080496329 title "Unions of sets of lengths" @default.
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- W2080496329 doi "https://doi.org/10.7169/facm/1229696561" @default.
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