Abstract
Every Krull monoid has a transfer homomorphism onto a monoid of zero-sum sequences over a subset of its class group. This transfer homomorphism is a crucial tool for studying the arithmetic of Krull monoids. In the present paper, we strengthen and refine this tool for Krull monoids with finitely generated class group.
Highlights
Transfer homomorphisms are a central tool in factorization theory
In the present paper we focus on transfer homomorphisms of Krull monoids
We show the same result for Krull monoids with finitely generated class group (Theorem 3.4)
Summary
Transfer homomorphisms are a central tool in factorization theory. Since they are essentially surjective and allow to lift factorizations, they make it possible to study the arithmetic of monoids and domains as follows. It is an easy observation to see that the inclusion B(G P ) → F(G P ), where F(G P ) is the free abelian monoid with basis G P , is a cofinal divisor homomorphism but in general not a divisor theory This means that B(G P ) is not optimal, neither from the algebraic point of view nor for arithmetical investigations. It turned out, first for special subsets of finite abelian groups, that it is possible to construct a new subset G P and a divisor homomorphism θ : H → B(G P ) such that B(G P ) → F(G P ) is a divisor theory. We demonstrate the usefulness of our construction in an example of a Krull monoid with infinite class group (Example 4.10)
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