Vol. 35, No. 3, 1970

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On the semigroup of binary relations

Robert James Plemmons and M. T. West

Vol. 35 (1970), No. 3, 743–753

The concepts of row and column bases for an element of X, the semigroup of binary relations on a set X, are introduced by interpreting a binary relation as a boolean matrix; these ideas are then used to characterize the Green’s equivalences on X. It is shown that the class of idempotent relations whose rows and columns form independent sets coincides with the class of partial order relations on subsets of X. Regularity in X is investigated using these results.

Mathematical Subject Classification
Primary: 20.93
Received: 5 January 1970
Published: 1 December 1970
Robert James Plemmons
M. T. West