Local and Global Tameness in Krull Monoids

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 equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then , where is the Davenport constant of G. We analyze the case when equals the lower bound, and we show that 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.

Key Words:

• Krull monoids
• Nonunique factorizations
• Tame degree
• Zero-sum subsequence

2010 Mathematics Subject Classification:

• 20M13
• 13A05
• 13F05
• 11B75
• 11B30

ACKNOWLEDGMENT

We thank the referees for reading the paper carefully. They have provided a list of helpful comments which, among others, led to a more general version of Lemma 4.3.

Notes

Communicated by F. Tartarone.

Dedicated to Marco Fontana on the occasion of his 65th birthday.