Abstract
We show that Krull's Separation Lemma for arbitrary rings and a certain lattice-theoretical generalization of it are equivalent to the classical Prime Ideal Theorem for Boolean algebras. As an application, we derive the intersection theorem for Baer radicals from choice principles weaker than the Axiom of Choice. A central tool for our considerations are Scott-openm-filters in quantales.
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Communicated by K. Keimel
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Banaschewski, B., Erné, M. On Krull's Separation Lemma. Order 10, 253–260 (1993). https://doi.org/10.1007/BF01110546
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DOI: https://doi.org/10.1007/BF01110546