Almost Injective Transformations of an Infinite Set |
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Authors: | Suzana Mendes-Gonçalves R. P. Sullivan |
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Affiliation: | 1. Centro de Matemática , Universidade do Minho , Braga , Portugal smendes@math.uminho.pt;3. School of Mathematics and Statistics , University of Western Australia , Nedlands , Australia |
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Abstract: | Let V be an infinite-dimensional vector space, let n be a cardinal such that ?0 ≤ n ≤ dim V, and let AM(V, n) denote the semigroup consisting of all linear transformations of V whose nullity is less than n. In recent work, Mendes-Gonçalves and Sullivan studied the ideal structure of AM(V, n). Here, we do the same for a similarly-defined semigroup AM(X, q) of transformations defined on an infinite set X. Although our results are clearly comparable with those already obtained for AM(V, n), we show that the two semigroups are never isomorphic. |
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Keywords: | Almost one-to-one transformations Green's relations Ideals |
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