Abstract
This is the extended and revised version of notes written for the Advanced Course in Combinatorics and Geometry: Additive Combinatorics. The course took place at the Centre de Recerca Matemàtica (CRM) at Barcelona in spring 2008. It gives a survey on the interaction between two, at first glance very disparate areas of mathematics: Non-Unique Factorization Theory (see [71, 70, 13, 87, 120]) and Additive Group Theory (see [103, 36, 104, 107, 23, 130, 52]). The main objective of factorization theory is a systematic treatment of phenomena related to the nonuniqueness of factorizations in monoids and integral domains. In the setting of Krull monoids (the main examples we have in mind are the multiplicative monoids of rings of integers of algebraic number fields) most problems can be translated into zero-sum problems over the class group. It will be a main aim of this course to highlight this relationship.
This work was supported by the Centre de Recerca Matemàtica (CRM) at Barcelona and by the Austrian Science Fund FWF, Project No. M1014-N13.
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(2009). Introduction. In: Combinatorial Number Theory and Additive Group Theory. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8962-8_1
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DOI: https://doi.org/10.1007/978-3-7643-8962-8_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8961-1
Online ISBN: 978-3-7643-8962-8
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