Arithmetic of Mori domains and monoids |
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Authors: | Alfred Geroldinger Wolfgang Hassler |
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Institution: | Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria |
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Abstract: | In this paper we introduce weakly C-monoids as a new class of v-noetherian monoids. Weakly C-monoids generalize C-monoids and make it possible to study multiplicative properties of a wide class of Mori domains, e.g., rings of generalized power series with coefficients in a field and exponents in a finitely generated monoid. The main goal of the paper is to study the question when a weakly C-monoid is locally tame. After having proved a classification theorem for local tameness, we use it to show that every locally tame weakly C-monoid whose complete integral closure has finite class group has finite catenary degree and finite set of distances. |
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