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21.—The Structure of certain Ordered Regular Semigroups*

  • T. S. Blyth (a1)

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.

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References

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1Blyth, T. S.. Dubreil-Jacotin inverse semigroups. Proc. Roy. Soc. Edinburgh. Sect. A. 71 (1974), 345360.
2Blyth, T. S. and Janowitz, M. F.. Residuation theory. Internal. Monographs Pure Appl. Math. 102 (Oxford: Pergamon, 1972).
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).
4Hall, T. E.. Orthodox semigroups and uniform and antiuniform bands. J. Algebra 16 (1970), 204217.
5McAlister, D. B.. Groups, semilattices and inverse semigroups II. Trans. Amer. Math. Soc. 192 (1974), 227244.
6Petrich, M.. Introduction to semigroups (Columbus, Ohio: Merrill, 1973).

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