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On the semigroup of
binary relations
Robert James Plemmons and M. T. West |
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Vol. 35 (1970), No. 3, 743–753
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Abstract |
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The concepts of row and column bases for an element of ℬX, 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 ℬX. 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 ℬX is investigated using these results. |
Mathematical Subject Classification
Primary: 20.93
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Milestones
Received: 5 January 1970
Published: 1 December 1970
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Authors |
| Robert James Plemmons | |
| M. T. West | |
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