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A description of E-unitary inverse semigroups

Published online by Cambridge University Press:  14 November 2011

Ross Wilkinson
Ross Wilkinson
Affiliation:
Monash University, Clayton, Australia3168
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Synopsis

An E-unitary inverse semigroup, S, has the property that, if x=S, and e2 = e=S, then (xe)2 = xe implies that x2 = x. As a consequence of this, we can see that S is an extension of its semilattice of idempotents, E, by its maximal group morphic image, G. Thus, following McAlister (1974), we attempt to describe S in terms of E and G. If we extend the semilattice E to a larger semilattice F, we are able to describe S in terms of a semi-direct product of F and G, giving a new interpretation to the approach of Schein (1975).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 239 - 242
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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