Weak representation theory in the calculus of relations

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2006-01-01
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Alm, Jeremy
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Roger D. Maddux
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Altmetrics
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Mathematics
Abstract

Relation algebras are abstractions of collections of binary relations under the operations of union, intersection, complementation, relational composition, inversion, and identity. A relation algebra is called representable if it is isomorphic to such a collection of relations. An algebra is called weakly representable if it is isomorphic to a collection of relations not necessarily closed under union and complementation. We consider weak representations over finite sets and note a connection between weak representations and relativizations. We also consider the question from Bjarni Jonsson's 1959 paper, whether the class of weakly representable relation algebras forms a variety. We show that it is, provided that a certain embedding condition obtains. Remaining open questions are collected in the concluding remarks.

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Sun Jan 01 00:00:00 UTC 2006