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Cancellation in the Stone–Čech compactification of a discrete semigroup

Published online by Cambridge University Press:  20 January 2009

Neil Hindman  and
Dona Strauss
Neil Hindman
Affiliation:
Department of Mathematics, Howard University, Washington D.C. 20059, U.S.A.
Dona Strauss
Affiliation:
Department of Pure Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX
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Abstract

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We investigate both left and right cancellation in the Stone–Čech compactification βS of a discrete semigroup S, obtaining several results for arbitrary semigroups S and others for more restricted semigroups. In particular, if S is the semigroup of injective functions from a set to itself we determine precisely which pairs x, y and S have some p∈βS with px = py. We also obtain several new results about right cancellation in (βℕ, +).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 3 , October 1994 , pp. 379 - 397
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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