Abstract
We show that each representation ϕ, say, of an inverse semigroup S, by means of transformations of a set X, determines a representation ϕ* by means of partial one-to-one transformations of X, in such a fashion that sϕ ↦ sϕ*, for s ∈ S, is an isomorphism of Sϕ upon Sϕ*. An immediate corollary is the classical faithful representation of an inverse semigroup as a semigroup of partial one-to-one transformations.
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J. Lambek and Z. Hedrlín.How comprehensive is the category of semigroups? J. Algebra 11(1969), 195–212.
G.B. Preston.Congruences on semigroups (p. 1). Lecture Notes, Pennsylvania State University, August 1963, 123 pp.+vi+D1–D15.
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Communicated by W.D. Munn
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Preston, G.B. Representations of inverse semigroups by one-to-one partial transformations of a set. Semigroup Forum 6, 240–245 (1973). https://doi.org/10.1007/BF02389127
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DOI: https://doi.org/10.1007/BF02389127