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Congruences on ωn-Bisimple Semigroups

Published online by Cambridge University Press:  09 April 2009

R. J. Warne
R. J. Warne
Affiliation:
West Virginia University Morgantown, West Virginia
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Let S be a bisimple semigroup and let Es denote its set of idempotents. We may partially order Es in the following manner: if e, f ∈ E s, e ≧ f if and only if ef = fe = e. We then say that Es is under or assumes its natural order. Let I0 denote the non-negative integers and let n denote a natural number. If Es, under its natural order, isomorphic to (I0)n under the reverse of the usual lexicographic order, we call S an ωn-bisimple semigroup. (See [9] for an explanation of notation.) We determined the structure of ωn-bisimple semigroups completely mod groups in [9]. The ωn-bisimple semigroups, the I-bisimple semigroups [8], and the ωnI-bisimple semigroups [9] are classes of simple semigroups except completely simple semigroups whose structure has been determined mod groups.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 257 - 274
Copyright
Copyright © Australian Mathematical Society 1969

References

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