On congruence half-factorial Krull monoids with cyclic class group
| Autor: | Wolfgang A. Schmid, Alain Plagne |
|---|---|
| Přispěvatelé: | Centre de Mathématiques Laurent Schwartz (CMLS), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), ANR-12-BS01-0011,CAESAR,Combinatoire Additive: Ensembles, Séquences et Applications Remarquables(2012) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Monoid
Pure mathematics [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] Dedekind domain Commutative Algebra (math.AC) MSC 11B30 13F05 01 natural sciences Prime (order theory) Factorization factorization 0103 physical sciences FOS: Mathematics Discrete Mathematics and Combinatorics Congruence (manifolds) Number Theory (math.NT) Ideal (ring theory) 0101 mathematics Algebraic number minimal distance Mathematics Algebra and Number Theory Krull monoid Mathematics - Number Theory Group (mathematics) 010102 general mathematics block monoid Mathematics - Commutative Algebra [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 010307 mathematical physics half-factorial zero-sum sequence set of lengths |
| Popis: | Journal of Combinatorial Algebra (to appear); We carry out a detailed investigation of congruence half-factorial Krull monoids of various orders with finite cyclic class group and related problems. Specifically, we determine precisely all relatively large values that can occur as a minimal distance of a Krull monoid with finite cyclic class group, as well as the exact distribution of prime divisors over the ideal classes in these cases. Our results apply to various classical objects, including maximal orders and certain semi-groups of modules. In addition, we present applications to quantitative problems in factorization theory. More specifically, we determine exponents in the asymptotic formulas for the number of algebraic integers whose sets of lengths have a large difference. |
| Databáze: | OpenAIRE |
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