Elasticity of factorizations in atomic monoids and integral domains

DOI10.5802/jtnb.147zbMath0844.11068OpenAlexW2069513340WikidataQ114013330 ScholiaQ114013330MaRDI QIDQ1910676

Franz Halter-Koch

Publication date: 1 September 1996

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1995__7_2_367_0

zbMATH Keywords

elasticityKrull domainatomic integral domaindivisor class groupatomic monoidslength of factorizationorders with finite elasticity

Mathematics Subject Classification ID

Units and factorization (11R27) Commutative Noetherian rings and modules (13E05) Integral domains (13G05)

Related Items (21)

Properties of factorizations with successive lengths in one-dimensional local domains ⋮ Chains of factorizations and sets of lengths ⋮ Differences in sets of lengths of Krull monoids with finite class group. ⋮ Generalized sets of lengths ⋮ On the primality and elasticity of algebraic valuations of cyclic free semirings ⋮ Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid ⋮ Elasticity of factorizations in \(R_{0}+XR_{1}+\cdots +X^{l}R_{l}[X\)] ⋮ A PRECISE RESULT ON THE ARITHMETIC OF NON-PRINCIPAL ORDERS IN ALGEBRAIC NUMBER FIELDS ⋮ Elasticity in certain block monoids via the Euclidean table ⋮ On the arithmetic of Krull monoids with infinite cyclic class group ⋮ Computing the elasticity of a Krull monoid ⋮ Long sets of lengths with maximal elasticity ⋮ On the delta set of a singular arithmetical congruence monoid. ⋮ The distribution of prime divisors in Krull monoid domains ⋮ Criteria for unique factorization in integral domains ⋮ Some remarks on half-factorial orders ⋮ ON DELTA SETS OF NUMERICAL MONOIDS ⋮ Inside factorial monoids and integral domains ⋮ An addition theorem and its arithmetical application ⋮ When is length a length function? ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Factorization problems in semigroups
• Discriminants of algebraic number fields
• Longueurs des décompositions en produits d'éléments irréductibles dans un anneau de Dedekind. (Lengths of decompositions in products of irreducible elements in a Dedekind ring)
• On non-unique factorizations into irreducible elements
• On the number and ideal theory of one-dimensional noetherian integral domains.
• An approximation theorem for semigroups with divisor theory
• Realization theorems for semigroups with divisor theory
• Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements
• On Davenport's constant
• Elasticity of factorizations in integral domains
• Arithmetical theory of monoid homomorphisms
• Elasticity of factorization in number fields
• On the arithmetic of certain not integrally closed noetheian integral domains
• Rational Elasticity of Factorizations in Krull Domains
• T-block monoids and their arithmetical applications to certain integral domains

This page was built for publication: Elasticity of factorizations in atomic monoids and integral domains