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The lattice of inverse subsemigroups of a reduced inverse semigroup†

Published online by Cambridge University Press:  18 May 2009

P. R. Jones
P. R. Jones
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, Australia,3168
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An inverse semigroup R is said to be reduced (or proper) if ℛ∩σ= i (where σ is the minimum group congruence on R). McAlister has shown ([3], [4]) that every reduced inverse semigroup is isomorphic with a “P-semigroup” P(G, , ), for some semilattice , poset containing as an ideal, and group G acting on by order-automorphisms; (and, conversely, every P-semigroup is reduced). In [4], he also found the morphisms between P-semigroups, in terms of morphisms between the respective groups, and between the respective posets.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 161 - 172
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

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