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arXiv · 1302.3078

Local and global tameness in Krull monoids

W. D. Gao·Alfred Geroldinger·Wolfgang Schmid
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Abstract

Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t (H) equals zero if and only if H is factorial (equivalently, |G|=1). If |G| > 1, then D (G) <= t (H) <= 1 + D (G) (D (G) -1) / 2, where D (G) is the Davenport constant of G. We analyze the case when t (H) equals the lower bound, and we show that t (H) grows asymptotically as the upper bound, when both terms are considered as functions of the rank of G. We provide more precise results if G is either cyclic or an elementary 2-group.

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W. D. Gao, Alfred Geroldinger, Wolfgang Schmid. 2013-02-13. Local and global tameness in Krull monoids. https://arxiv.org/abs/1302.3078

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