Applied Categorical Structures

, Volume 8, Issue 1, pp 115–144

Prime Ideal Theory for General Algebras

Authors

  • Marcel Erné
    • Department of MathematicsUniversity of Hannover
Article

DOI: 10.1023/A:1008611926427

Cite this article as:
Erné, M. Applied Categorical Structures (2000) 8: 115. doi:10.1023/A:1008611926427
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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).

closure systemcm-latticedistributiveideallocaleprimequantaleradicalresiduatedsemiprime
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© Kluwer Academic Publishers 2000