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V-regular semigroups

Published online by Cambridge University Press:  14 November 2011

K. S. S. Nambooripad  and
F. Pastijn
K. S. S. Nambooripad
Affiliation:
Department of Mathematics, University of Kerala, Kariavattom 695-591, India
F. Pastijn
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 271, B-9000 Gent, Belgium
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Synopsis

A regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents. The strongly V-regular semigroups form a subclass of the class of V-regular semigroups which may be characterized in terms of their biordered set of idempotents. It is shown that the class of strongly V-regular semigroups comprises the elementary rectangular bands of inverse semigroups (including the completely simple semigroups), a special class of orthodox semigroups (including the inverse semigroups), the strongly regular Baer semigroups (including the semigroups that are the multiplicative semigroup of a von Neumann regular ring), the full transformation semigroup on a set, and the semigroup of all partial transformations on a set.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 275 - 291
Copyright
Copyright © Royal Society of Edinburgh 1981

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