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E-unitary inverse semigroups over semilattices

Published online by Cambridge University Press:  18 May 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115, U.S.A.
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An inverse semigroup is called E-unitary if the equations ea = e = e2 together imply a2 = a. In a previous paper [4], the author showed that any E-unitary inverse semigroup is isomorphic to a semigroup constructed from a triple (G, ℋ, ) consisting of a down-directed partially ordered set ℋ, an ideal and subsemilattice of ℋ and a group G acting on ℋ, on the left, by order automorphisms in such a way that ℋ = G. This semigroup is denoted by P(G, ℋ, ); it consists of all pairs (a, g)∈ × G such that g−1a ∈ , under the multiplication

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 1 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

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