Bifunctional-elementary relation algebras

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A relation algebra is bifunctional-elementary if it is atomic and for any atom a, the element a;1;a is the join of at most two atoms, and one of these atoms is bifunctional (an element x is bifunctional if x;x̌ + x̌ ;x ≤ 1'). We show that bifunctional-elementary relation algebras are representable. Our proof combines the representation theorems for: pair-dense relation algebras given by R. Maddux; relation algebras generated by equivalence elements provided corresponding relativizations are representable by S. Givant; and strong-elementary relation algebras dealt with in our earlier work. It turns out that atomic pair-dense relation algebras are bifunctional elementary, showing that our theorem generalizes the representation theorem of atomic pair-dense relation algebras. The problem is still open whether the related classes of rather elementary, functional-elementary, and strong functional-elementary relation algebras are representable.

Original languageEnglish
Pages (from-to)425-438
Number of pages14
JournalAlgebra Universalis
Issue number4
Publication statusPublished - May 2009


  • Bifunctional-elementary
  • Pair-dense.
  • Relation algebras
  • Representable relation algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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