The Semigroup of Binary Relations

Speaker: Stewart Wilcox, University of Sydney

Abstract:A binary relation on a set I is a subset of I × I . Under composition, the set of all binary relations forms a semigroup B_I . We can also interpret B_I as the semigroup of boolean matrices. In this talk we give an introductory exposition of the properties of B_I from a semigroup theoretic point of view. We characterise Green's relations and regularity, and discuss certain idempotents.