## Abstract

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 language | English |
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Pages (from-to) | 425-438 |

Number of pages | 14 |

Journal | Algebra Universalis |

Volume | 60 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2009 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory