Abstract
We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).
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Erné, M. Prime Ideal Theory for General Algebras. Applied Categorical Structures 8, 115–144 (2000). https://doi.org/10.1023/A:1008611926427
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DOI: https://doi.org/10.1023/A:1008611926427