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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.

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

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