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Principally ordered regular semigroups

Published online by Cambridge University Press:  18 May 2009

T. S. Blyth  and
G. A. Pinto
T. S. Blyth
Affiliation:
Department of Mathematical Sciences, University of St Andrews, St Andrews KY16 9SS, Fife, Scotland.
G. A. Pinto
Affiliation:
Departamento de Matematica, Universidade Nova de Lisboa, 2825 Monte da Caparica, Portugal.
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An ordered semigroup S will be called principally ordered if, for every x ɛ S, there exists

x* = max {y ɛ S; xyx ≤ x}.

Here we shall be concerned with the case where S is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by V(x) the set of inverses of x ɛ S.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 349 - 364
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Blyth, T. S. and Janowitz, M. F., Residuation Theory, Pergamon Press, 1972.Google Scholar
2.Blyth, T. S., Perfect Dubreil-Jacotin semigroups. Proc. Roy. Soc. Edinburgh, 78A, 1977, 101–104.Google Scholar
3.Blyth, T. S. and McFadden, R., Naturally ordered regular semigroups with a greatest idempotent. Proc. Roy. Soc. Edinburgh, 91A, 1981, 107–122.Google Scholar
4.Blyth, T. S. and McFadden, R., On the construction of a class of regular semigroups. Journal of Algebra, 81, 1983, 1–22.CrossRefGoogle Scholar
5.Fitz-Gerald, D. G., On inverses of products of idempotents in regular semigroups. J. Austral. Math. Soc., 13, 1972, 335–337.Google Scholar
6.McAlister, D. B., Regular Rees matrix semigroups and Dubreil-Jacotin semigroups. J. Austral. Math. Soc., 31, 1981, 325–336.CrossRefGoogle Scholar
7.Saito, Tatsuhiko, Naturally ordered regular semigroups with maximum inverses. Proc. Edinburgh Math. Soc., 32, 1989, 33–39.CrossRefGoogle Scholar