On a general theory of factorization in integral domains

DOI10.1216/RMJ-2011-41-3-663zbMath1228.13001OpenAlexW2048064275MaRDI QIDQ633909

Andrea M. Frazier, Daniel D. Anderson

Publication date: 2 August 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2011-41-3-663

zbMATH Keywords

factorizationintegral domain\(\tau\)-factorization\(\tau\)-irreducible element\(\tau\)-prime element

Mathematics Subject Classification ID

Integral domains (13G05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Divisibility and factorizations in commutative rings (13A05) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items

\(\tau\)-regular factorization in commutative rings with zero-divisors ⋮ Three frameworks for a general theory of factorization ⋮ Two counterexamples in abstract factorization ⋮ Unique Factorization in Torsion-Free Modules ⋮ On the characterization of \(\tau_{(n)}\)-atoms ⋮ $\tau$-Atomicity and Quotients of Size Four ⋮ Generalized Irreducible Divisor Graphs

Cites Work

• Factorization in integral domains
• On the converse of a well-known fact about Krull domains
• Principal ideal rings and a condition of Kummer
• On primary factorizations
• Elasticity of factorizations in integral domains
• Factorization in integral domains. II
• Semirigid GCD domains
• Irreducible divisors in domains of finite character
• Factorization in commutative rings with zero divisors
• Half-factorial-domains
• Unique comaximal factorization
• Half factorial domains
• Schreier Rings
• Two star-operations and their induced lattices
• Ont-invertibility III
• Finite factorization domains
• A Characterization of Algebraic Number Fields with Class Number Two
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