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Perfect Dubreil-Jacotin semigroups*

Published online by Cambridge University Press:  14 February 2012

T. S. Blyth
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
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Synopsis

We determine a set of conditions that are necessary and sufficient for an ordered regular semigroup to be a perfect Dubreil-Jacotin semigroup; and a necessary and sufficient condition for a perfect Dubreil-Jacotin semigroup to be orthodox.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 1-2 , 1977 , pp. 101 - 104
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Blyth, T. S. and Janowitz, M. F.Residuation theory (Oxford: Pergamon, 1972).Google Scholar
2Blyth, T. S.Dubreil-Jacotin inverse semigroups. Proc. Roy. Soc. Edinburgh Sect. A 71 (1974), 345–360.Google Scholar
3Blyth, T. S.The structure of certain ordered regular semigroups. Proc. Roy. Soc. Edinburgh Sect. A 75 (1976), 235–257.CrossRefGoogle Scholar
4Blyth, T. S.On a class of Dubreil-Jacotin regular semigroups and a construction of Yamada. Proc. Roy. Soc. Edinburgh Sect. A, 77 (1977) 145–150.CrossRefGoogle Scholar
5McAliste, D. B.: and Blyth, T. S. Split orthodox semigroups. J. Algebra, to appear.Google Scholar