Partial actions and an embedding theorem for inverse semigroups
- 7 Downloads
We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O’Carroll’s theorem on idempotent pure extensions of inverse semigroups.
KeywordsInverse semigroup Premorphism Idempotent pure congruence
The author thanks the referee for the very detailed reading of the manuscript and numerous useful suggestions which permitted to simplify and shorten the proofs. In particular, the use of [6, Proposition 1.2.1] in the proofs of Lemmas 2.1 and 2.2, as well as the use of the order-preserving property of \(\tau _t\) in the proof of Lemma 2.6 are due to the referee. Section 4 also arose from referee’s comments.
This work was partially supported by FAPESP of Brazil (process number: 2012/01554–7).
- 7.M.V. Lawson, Margolis, S.W, In McAlister’s footsteps: a random ramble around the \(P\) -theorem, in Semigroups and Formal Languages (World Scientific Publishing, Hackensack, 2007), pp. 145–163Google Scholar
- 13.M. Petrich, Inverse Semigroups. Pure and Applied Mathematics (Wiley, New York, 1984)Google Scholar