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Bisimple weakly inverse semigroups with partial right unitoids

Published online by Cambridge University Press:  18 May 2009

S. Madhavan
S. Madhavan
Affiliation:
Department of Mathematics, University College, Trivandrum 695 034, Kerala, South India
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In an earlier paper [5] of the author bisimple weakly inverse semigroups with partial identities were studied. The aim of this paper is to extend the results to a wider class of semigroups, viz: bisimple weakly inverse semigroups with partial right unitoids. It is found that an ℛ-class of weakly inverse semigroup is a right skew groupoid R = (R, P), where P is a right skew semigroup [5], P⊆R, and R is a partial semigroup satisfying certain conditions. When S is a bisimple weakly inverse semigroup with E the set of partial right unitoids, it can be shown that the ℛ-class R = (R, P) containing E, which is a right skew groupoid, satisfies the following:

(i) for any a, b ∈ R, there exists c ∈ R such that Pa ∩ Pb = Pc;

(ii) for any a ∈ R, there exists a left identity e of R such that (Pa ∩ P)e = Pa ∩ P.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 1 - 10
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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