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Biordered sets are biordered subsets of idempotents of semigroups

Part of: Semigroups Ordered sets

Published online by Cambridge University Press:  09 April 2009

David Easdown
David Easdown
Affiliation:
Department of Mathematics Monash UniversityClayton, VictoriaAustralia3168
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Abstract

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A new arrow notation is used to describe biordered sets. Biordered sets are characterized as biordered subsets of the partial algebras formed by the idempotents of semigroups. Thus it can be shown that in the free semigroup on a biordered set factored out by the equations of the biordered set there is no collapse of idempotents and no new arrows.

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20M10: General structure theory 20M30: Representation of semigroups; actions of semigroups on sets 06A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 258 - 268
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Easdown, D. and Hall, T. E., ‘Reconstructing some idempotent-generated semigroups from their biordered sets’, Semigroup Forum, to appear.Google Scholar
[2]Nambooripad, K. S. S., ‘Structure of regular semigroups I’, Mem. Amer. Math. Soc. 22 (1979), no. 224.Google Scholar
[3]Pastijn, F., ‘The Biorder on the partial groupoid of idempotents of a semigroup’, J. Algebra 65 (1980), 147–187.Google Scholar