Irreducible Factorization Lengths and the Elasticity Problem within ℕ

Irreducible Factorization Lengths and the Elasticity Problem within ℕ

A large class of multiplicative submonoids of the natural numbers is presented, which includes congruence monoids as well as numerical monoids (by isomorphism). For monoids in this class, the important factorization property of finite elasticity is characterized.

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Veröffentlicht in:The American mathematical monthly 2013-04, Vol.120 (4), p.322-328
Hauptverfasser: Jenssen, Matthew, Montealegre, Daniel, Ponomarenko, Vadim
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Arithmetic
Atoms
Elasticity
Factorization
Integers
Mathematical congruence
Mathematical problems
Mathematical theorems
Monoids
Numerical analysis
Semigroups
Submonoids
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Beschreibung
Zusammenfassung:A large class of multiplicative submonoids of the natural numbers is presented, which includes congruence monoids as well as numerical monoids (by isomorphism). For monoids in this class, the important factorization property of finite elasticity is characterized.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.120.04.322