Radical factorization in commutative rings, monoids and multiplicative lattices

DOI10.1007/s00012-019-0597-1zbMath1420.13008arXiv1811.00242OpenAlexW2898885889WikidataQ127799737 ScholiaQ127799737MaRDI QIDQ2418563

Andreas Reinhart, Bruce Olberding

Publication date: 27 May 2019

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

Full work available at URL: https://arxiv.org/abs/1811.00242

zbMATH Keywords

monoidcomplete multiplicative latticeideal systemradical factorizationSP-monoid

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Arithmetic theory of semigroups (20M13)

Related Items (6)

Products of ideals in Leavitt path algebras ⋮ A Bazzoni-Type Theorem for Multiplicative Lattices ⋮ Commutative rings with absorbing factorization ⋮ Factorization theory in commutative monoids ⋮ Radical factorization in finitary ideal systems ⋮ A class of multiplicative lattices

Cites Work

• Factoring ideals in integral domains
• Manis valuations and Prüfer extensions. I: A new chapter in commutative algebra
• Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings
• Abstract commutative ideal theory
• Abstract commutative ideal theory without chain condition
• Dilworth's principal elements
• Almost principal element lattices
• \(s\)-prime elements in multiplicative lattices
• Group-theoretic and topological invariants of completely integrally closed Prüfer domains
• On Monoids and Domains Whose Monadic Submonoids Are Krull
• Bézout SP-Domains
• Factoring Ideals into Semiprime Ideals
• Semiprime factorizations in unions of Dedekind domains.
• Principal element lattices
• SP-rings with zero-divisors
• Principal Elements of Lattices of Ideals
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