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21.—The Structure of certain Ordered Regular 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

In a previous publication [1] we determined the structure of some new types of ordered inverse semigroup in which the ordering need not be the natural ordering. At the moment, very little is known about ordered regular semigroups and the purpose of this paper is to generalise the structure theorems in [1] to corresponding theorems on ordered regular semigroups. The results obtained provide an interesting bridge between the theory of semigroups and that of ordered semigroups, these theories currently having very little in common.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 3 , 1976 , pp. 235 - 257
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

REFERENCES

1Blyth, T. S.. Dubreil-Jacotin inverse semigroups. Proc. Roy. Soc. Edinburgh. Sect. A. 71 (1974), 345–360.Google Scholar
2Blyth, T. S. and Janowitz, M. F.. Residuation theory. Internal. Monographs Pure Appl. Math. 102 (Oxford: Pergamon, 1972).Google Scholar
3Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, I and II. Math. Surveys, 7 (Providence: R.I.: Amer. Math. Soc, 1961 and 1967).Google Scholar
4Hall, T. E.. Orthodox semigroups and uniform and antiuniform bands. J. Algebra 16 (1970), 204–217.Google Scholar
5McAlister, D. B.. Groups, semilattices and inverse semigroups II. Trans. Amer. Math. Soc. 192 (1974), 227–244.Google Scholar
6Petrich, M.. Introduction to semigroups (Columbus, Ohio: Merrill, 1973).Google Scholar