Bifunctional-elementary relation algebras |
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Authors: | Mohamed El Bachraoui |
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Affiliation: | (1) Dept. Mathematical Sciences, United Arab Emirates University, PO Box 17551, Al-Ain, UAE |
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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 ’). 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. Received July 15, 2007; accepted in final form March 17, 2008. |
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Keywords: | KeywordHeading" >2000 Mathematics Subject Classification: 03G15 03G25 |
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