On the atomicity of monoid algebras

DOI10.1016/j.jalgebra.2019.07.033zbMath1442.20039arXiv1906.11138OpenAlexW2967279323WikidataQ127368541 ScholiaQ127368541MaRDI QIDQ2326438

Felix Gotti, Coykendall, Jim

Publication date: 7 October 2019

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.11138

zbMATH Keywords

monoid algebrasatomicityatomic algebrasatomic Puiseux monoids

Mathematics Subject Classification ID

Commutative semigroups (20M14) Integral domains (13G05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Semigroup rings, multiplicative semigroups of rings (20M25)

Related Items (33)

Factorization invariants of the additive structure of exponential Puiseux semirings ⋮ Atomic semigroup rings and the ascending chain condition on principal ideals ⋮ Unnamed Item ⋮ On the additive structure of algebraic valuations of polynomial semirings ⋮ Length-factoriality in commutative monoids and integral domains ⋮ Unnamed Item ⋮ Arithmetic of additively reduced monoid semidomains ⋮ On the arithmetic of polynomial semidomains ⋮ Unnamed Item ⋮ A characterisation of atomicity ⋮ On the atomic structure of torsion-free monoids ⋮ Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid ⋮ Factorizations in upper triangular matrices over information semialgebras ⋮ When Is a Group Algebra Antimatter? ⋮ Irreducibility and Factorizations in Monoid Rings ⋮ On the Molecules of Numerical Semigroups, Puiseux Monoids, and Puiseux Algebras ⋮ On strongly primary monoids, with a focus on Puiseux monoids ⋮ A Note on Fraction Decompositions of Integers ⋮ On the atomic structure of exponential Puiseux monoids and semirings ⋮ A characterization of weakly Krull monoid algebras ⋮ Bi-atomic classes of positive semirings ⋮ Factorization theory in commutative monoids ⋮ Divisibility in rings of integer-valued polynomials ⋮ Bounded and finite factorization domains ⋮ On the set of molecules of numerical and Puiseux monoids ⋮ Atomicity and density of Puiseux monoids ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors ⋮ Integral domains and the IDF property ⋮ When Is a Puiseux Monoid Atomic? ⋮ Hereditary atomicity in integral domains ⋮ On atomic density of numerical semigroup algebras ⋮ On semigroup algebras with rational exponents ⋮ Finite factorization properties in commutative monoid rings with zero divisors

Cites Work

• Factorization in integral domains
• Increasing positive monoids of ordered fields are FF-monoids
• On the atomic property for power series rings
• Polynomial extensions of atomic domains
• FACTORIZATION IN MONOID DOMAINS
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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