Abstract
The prime ideal theorem for distributive lattices (PIT) is shown to imply that any complete distributive lattice with a compact unit has a prime element, which is then used to deduce from PIT that (1) every nontrivial ring with unit has a prime ideal, and (2) every Wallman locale is spatial.
AMS (MOS) subject classifications (1980)
03E25 06D99 16A66Key words
Prime Ideal Theorem Boolean Ultrafilter Theorem distributive lattice prime ideals in ringsPreview
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© D. Reidel Publishing Company 1985