Abstract
Let V be an infinite-dimensional vector space, let n be a cardinal such that ℵ0 ≤ 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.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
The authors acknowledge the support of the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI.
Notes
Communicated by V. Gould.
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