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On quasi-F-orthodox semigroups

Published online by Cambridge University Press:  20 January 2009

Bernd Billhardt  and
Mária B. Szendrei
Bernd Billhardt
Affiliation:
Fachbereich Mathematik, Gesamthochschule Kassel, Holländische Str. 36, D-W-34109 Kassel, Germany
Mária B. Szendrei
Affiliation:
Bolyai Institute, József Attila University, Aradi Vértanúk Tere 1, H-6720 Szeged, Hungary
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Abstract

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An orthodox semigroup S is termed quasi-F-orthodox if the greatest inverse semigroup homomorphic image of S1 is F-inverse. In this paper we show that each quasi-F-orthodox semigroup is embeddable into a semidirect product of a band by a group. Furthermore, we present a subclass in the class of quasi-F-orthodox semigroups whose members S are embeddable into a semidirect product of a band B by a group in such a way that B belongs to the band variety generated by the band of idempotents in S. In particular, this subclass contains the F-orthodox semigroups and the idempotent pure homomorphic images of the bifree orthodox semigroups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 361 - 385
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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