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On a class of Dubreil-Jacotin regular semigroups and a construction of Yamada*

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

In the publication [2] we obtained some structure theorems for certain Dubreil-Jacotin regular semigroups. A crucial observation in the course of investigating these types of ordered regular semigroups was that the (ordered) band of idempotents was normal. This is characteristic of a class of semigroups studied by Yamada [5] and called generalised inverse semigroups. Here we specialise a construction of Yamada to obtain a structure theorem that complements those in [2], The important feature of the present approach is the part played by the greatest elements that exist in each of the components in the semilattice decompositions involved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 145 - 150
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Blyth, T. S.Dubreil-Jacotin inverse semigroups. Proc. Roy. Soc. Edinburgh Sect. A 71 (1973), 345–360.Google Scholar
2Blyth, T. S.The structure of certain ordered regular semigroups. Proc. Roy. Soc. Edinburgh Sect. A 75 (1976), 235–257.CrossRefGoogle Scholar
3Blyth, T. S. and Janowitz, M. F.Residuation theory (Oxford: Pergamon, 1972).Google Scholar
4Petrich, M.Introduction to semigroups (Columbus: Merrill, 1973).Google Scholar
5Yamada, M.Regular semigroups whose idempotents satisfy permutation identities. Pacific J. Math. 21 (1967), 371–392.CrossRefGoogle Scholar