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Maximum idempotents in naturally ordered regular semigroups

Published online by Cambridge University Press:  20 January 2009

D. B. McAlister  and
R. McFadden
D. B. McAlister
Affiliation:
Department of Mathematical Sciences, Northern Illinois UniversityDeKalb, Illinois 60115, U.S.A.
R. McFadden
Affiliation:
Department of Mathematical Sciences, Northern Illinois UniversityDeKalb, Illinois 60115, U.S.A.
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We shall denote by ω the natural partial order on the idempotents E = E(S) of a regular semigroup S, so that in E,

A partially ordered semigroup S(≦) is called naturally partially ordered [9] if the imposed partial order ≦ extends ω in the sense that

No assumption is made about the reverse implication.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 213 - 220
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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