Applied Categorical Structures

, Volume 8, Issue 1, pp 115-144

First online:

Prime Ideal Theory for General Algebras

  • Marcel ErnéAffiliated withDepartment of Mathematics, University of Hannover

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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).

closure system cm-lattice distributive ideal locale prime quantale radical residuated semiprime