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Idempotent-Separating Extensions Of Inverse Semigroups

Published online by Cambridge University Press:  09 April 2009

H. D'Alarcao
H. D'Alarcao
Affiliation:
S.U.N.Y. at Stony Brook
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Extensions of semigroups have been studied from two points of view; ideal extensions and Schreier extension. In this paper another type of extension is considered for the class of inverse semigroups. The main result (Theorem 2) is stated in the form of the classical treatment of Schreier extensions (see e.g.[7]). The motivation for the definition of idempotentseparating extension comes primarily from G. B. Preston's concept of a normal set of subsets of a semigroup [6]. The characterization of such extensions is applied to give another description of bisimple inverse ω-semigroups, which were first described by N. R. Reilly [8]. The main tool used in the proof of Theorem 2 is Preston's characterization of congruences on an inverse semigroup [5]. For the standard terminology used, the reader is referred to [1].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 211 - 217
Copyright
Copyright © Australian Mathematical Society 1969

References

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