Prime elements from prime ideals

DOI10.1007/BF00334858zbMath0576.06010OpenAlexW2045952920MaRDI QIDQ1065041

Bernhard Banaschewski

Publication date: 1985

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00334858

zbMATH Keywords

Axiom of ChoicePrime Ideal TheoremAlmost Maximal Ideal Theoremdistributive complete lattices with compact unitsPrime Element Theorem

Mathematics Subject Classification ID

Structure and representation theory of distributive lattices (06D05) Lattice ideals, congruence relations (06B10) Axiom of choice and related propositions (03E25)

Related Items

The strength of prime separation, sobriety, and compactness theorems, The prime ideal theorem and representation of \(F\)-rings, More on the strength of Engeler's lemma., On the least multiplicative nucleus of a ring, Semidistributivity, prime ideals and the subbase lemma, Ideal completion and Stone representation of ideal-distributive ordered sets, Primes, irreducibles and extremal lattices, Compact Hausdorff approach frames, Finiteness conditions and distributive laws for Boolean algebras, On Krull's separation lemma

Cites Work

• Sur le théorème de Zorn
• Lattice Aspects of Radical Ideals and Choice Principles
• Prime ideals yield almost maximal ideals
• Unnamed Item