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Residuated regular semigroups

Published online by Cambridge University Press:  20 January 2009

T. S. Blyth  and
G. A. Pinto
T. S. Blyth
Affiliation:
Mathematical InstituteUniversity of St AndrewsScotland
G. A. Pinto
Affiliation:
Departamento de MatemáticaUniversidade Nova de LisboaPortugal
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Abstract

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We prove that in a residuated regular semigroup the elements of the form and are idempotents, and derive some consequences of this fact. In particular, we show how the maximality of such idempotents is related to the semigroup being naturally ordered, and obtain from this a characterisation of the boot-lace semigroup of [2].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 501 - 509
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Blyth, T. S. and Janowitz, M. F., Residuation Theory (Pergamon Press, 1972).Google Scholar
2.Blyth, T. S. and Pinto, G. A., Principally ordered regular semigroups, Glasgow Math. J. 32 (1990), 349–364.CrossRefGoogle Scholar
3.Blyth, T. S. and Pinto, G. A., Idempotents in principally ordered regular semigroups, Comm. Algebra 19 (1991), 1549–1563.CrossRefGoogle Scholar
4.Saito, Tatsuhiko, Naturally ordered regular semigroups with maximum inverses, Proc. Edinburgh Math. Soc. 32 (1989), 33–39.CrossRefGoogle Scholar