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Mitsch’s order and inclusion for binary relations and partitions

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Abstract

Mitsch’s natural partial order on the semigroup of binary relations is here characterised by equations in the theory of relation algebras. The natural partial order has a complex relationship with the compatible partial order of inclusion, which is explored by means of a sublattice of the lattice of preorders on the semigroup. The corresponding sublattice for the partition monoid is also described.

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Notes

  1. It would be better, to avoid possible confusion, to name these bipartitions of X, as suggested by J. D. Mitchell. For now, we persist with the customary name.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, 7001, Australia

    D. G. FitzGerald

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  1. D. G. FitzGerald
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Correspondence to D. G. FitzGerald.

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Communicated by Norman R. Reilly.

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FitzGerald, D.G. Mitsch’s order and inclusion for binary relations and partitions. Semigroup Forum 87, 161–170 (2013). https://doi.org/10.1007/s00233-012-9453-8

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  • DOI: https://doi.org/10.1007/s00233-012-9453-8

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