FACTORIZATION IN MONOID DOMAINS

DOI10.1081/AGB-100002153zbMath1009.13005MaRDI QIDQ2755354

Hwankoo Kim

Publication date: 22 April 2003

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

zbMATH Keywords

factorizationbounded factorization domainmonoid domains

Mathematics Subject Classification ID

Group rings (16S34) Integral domains (13G05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Divisibility and factorizations in commutative rings (13A05)

Related Items (13)

Atomic semigroup rings and the ascending chain condition on principal ideals ⋮ Factorization of polynomials with rational exponents over a field ⋮ On the \(S\)-class group of the monoid algebra \(D[\Gamma\)] ⋮ Bounded Factorization and the Ascending Chain Condition on Principal Ideals in Generalized Power Series Rings ⋮ Irreducibility and Factorizations in Monoid Rings ⋮ Long length functions ⋮ The ascending chain condition for principal left or right ideals of skew generalized power series rings. ⋮ On the atomicity of monoid algebras ⋮ Bounded and finite factorization domains ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors ⋮ Generalized power series with a limited number of factorizations ⋮ On semigroup algebras with rational exponents ⋮ Finite factorization properties in commutative monoid rings with zero divisors

Cites Work

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• Factorization in integral domains
• Atomic rings without a.c.c. on principal ideals
• Splitting the t-class group
• Finiteness theorems for factorizations
• Factorization in integral domains. II
• Irreducible divisors in domains of finite character
• Criteria for unique factorization in integral domains
• Factorization in integral domains. III
• Half-factorial-domains
• Divisibility properties in semigroup rings
• Polynomial extensions of atomic domains
• Torsion-free Abelian Semigroup Rings VI
• Half factorial domains
• Torsion-Free Abelian Group Rings III
• Finite factorization domains

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