Irreducibility and Factorizations in Monoid Rings

DOI10.1007/978-3-030-40822-0_9zbMath1472.13033arXiv1905.07168OpenAlexW2945346304MaRDI QIDQ5115894

Felix Gotti

Publication date: 21 August 2020

Published in: Numerical Semigroups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07168

zbMATH Keywords

Gauss lemmanumerical semigroupsmonoid algebrasatomic domainsPuiseux monoidsEisenstein's criterionother-half-factorial monoidsPuiseux algebras

Mathematics Subject Classification ID

Commutative semigroups (20M14) Integral domains (13G05) Semigroup rings, multiplicative semigroups of rings (20M25) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Arithmetic theory of semigroups (20M13)

Related Items (13)

On the additive structure of algebraic valuations of polynomial semirings ⋮ Factorizations in evaluation monoids of Laurent semirings ⋮ Length-factoriality in commutative monoids and integral domains ⋮ Factorization of polynomials with rational exponents over a field ⋮ Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid ⋮ Length-factoriality and pure irreducibility ⋮ A characterization of weakly Krull monoid algebras ⋮ Bi-atomic classes of positive semirings ⋮ A characterization of length-factorial Krull monoids ⋮ Bounded and finite factorization domains ⋮ On the set of molecules of numerical and Puiseux monoids ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors ⋮ On semigroup algebras with rational exponents

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