Prime elements from prime ideals
In the summer of 1984 A. R. Blass proved that the ''Almost Maximal Ideal Theorem'' which had been introduced by the reviewer [Fundam. Math. 123, 197-209 (1984; Zbl 0552.06004)] - and which he had previously believed to be a choice principle intermediate between the Prime Ideal Theorem and the Axiom of Choice - was in fact logically equivalent to the Prime Ideal Theorem. Blass' proof was a slightly involved one making use of the compactness theorem for first-order logic; on receiving news of it, both B. Banaschewski and the reviewer independently discovered simpler proofs. Here is Banaschewski's proof, which goes by way of a ''Prime Element Theorem'' for distributive complete lattices with compact units.
distributive complete lattices with compact units
scientific article; zbMATH DE number 3920543