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International Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 3, Pages 393-396

A simplification of D'Alarcao's idempotent separating extensions of inverse semigroups

Department of Mathematical Sciences, Indiana University-Purdue University at Fort Wayne, Fort Wayne 46805, Indiana, USA

Received 29 August 1977

Copyright © 1978 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In [2] D'Alarcao states necessary and sufficient conditions for the attainment of an idempotent-separating extension of an inverse semigroup. To do this D'Alarcao needed essentially three mappings satisfying thirteen conditions. In this paper we show that one can achieve the same results with two mappings satisfying eight conditions.