DMCA
Pair-Dense Relation Algebras (1991)
| Venue: | Transactions of the American Mathematical Society |
| Citations: | 83 - 9 self |
BibTeX
@TECHREPORT{Maddux91pair-denserelation,
author = {Roger Maddux},
title = {Pair-Dense Relation Algebras},
institution = {Transactions of the American Mathematical Society},
year = {1991}
}
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Abstract
The central result of this paper is that every pair-dense relation algebra is completely representable. A relation algebra is said to be pair-dense if every nonzero element below the identity contains a "pair". A pair is the relation algebraic analogue of a relation of the form fha; ai ; hb; big (with a = b allowed). In a simple pair-dense relation algebra, every pair is either a "point" (an algebraic analogue of fha; aig) or a "twin" (a pair which contains no point). In fact, every simple pairdense relation algebra A is completely representable over a set U iff jU j = + 2, where is the number of points of A and is the number of twins of A.
