The system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid

DOI10.1142/S0219498820501376zbMath1471.20039arXiv1806.11273OpenAlexW2962836151WikidataQ114614618 ScholiaQ114614618MaRDI QIDQ3303802

Felix Gotti

Publication date: 4 August 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.11273

zbMATH Keywords

elasticityconvex geometryfactorization theoryset of lengthsatomic monoidfree commutative monoid

Mathematics Subject Classification ID

Commutative semigroups (20M14) Free semigroups, generators and relations, word problems (20M05) Arithmetic theory of semigroups (20M13)

Related Items (12)

Finiteness of elasticities of orders in central simple algebras ⋮ Atoms of root-closed submonoids of \(\mathbb{Z}^2\) ⋮ Unnamed Item ⋮ On the primality and elasticity of algebraic valuations of cyclic free semirings ⋮ ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS ⋮ Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid ⋮ On strongly primary monoids, with a focus on Puiseux monoids ⋮ A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions ⋮ Bi-atomic classes of positive semirings ⋮ Factorization invariants of Puiseux monoids generated by geometric sequences ⋮ On the set of molecules of numerical and Puiseux monoids ⋮ When Is a Puiseux Monoid Atomic?

Uses Software

• MathOverflow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
• Atomicity and boundedness of monotone Puiseux monoids
• On the delta set of a singular arithmetical congruence monoid.
• Numerical semigroups.
• Unions of sets of lengths.
• Some factorization properties of Krull domains with infinite cyclic divisor class group
• Systems of sets of lengths of Puiseux monoids
• A realization theorem for sets of lengths in numerical monoids
• On the set of elasticities in numerical monoids
• Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
• Sets of arithmetical invariants in transfer Krull monoids
• On the arithmetic of strongly primary monoids.
• Full elasticity in atomic monoids and integral domains.
• Elasticity of factorization in number fields
• Measuring primality in numerical semigroups with embedding dimension three
• Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators
• Polytopes, Rings, and K-Theory
• Rational Elasticity of Factorizations in Krull Domains
• Factorization in Krull monoids with infinite class group
• Sets of Lengths
• On the atomic structure of Puiseux monoids
• A Characterization of Algebraic Number Fields with Class Number Two
• On delta sets and their realizable subsets in Krull monoids with cyclic class groups
• Computing the elasticity of a Krull monoid

This page was built for publication: The system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid