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TitleInverse semigroups generated by linear transformations
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
KeywordsInverse linear transformation semigroups
Issue date2005
PublisherAustralian Mathematical Society
JournalBulletin of the Australian Mathematical Society
Citation"Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 71 (2005) 205-213.
Abstract(s)Suppose X is a set with cardinal p and let q be an infinite cardinal less or equal than p. Let B=BL(p,q) denote the Baer-Levi semigroup defined on X. In 1984, Howie and Marques-Smith showed that, if p=q, then BB^{-1}=I(X), the symmetric inverse semigroup on X, and they described the subsemigroup of I(X) generated by B^{-1}B. In 1994, Lima extended that work to `independence algebras', and thus also to vector spaces. In this paper, we answer the natural question: what happens when p>q? We also show that, in this case, the analogues BB^{-1} for sets and GG^{-1} for vector spaces are never isomorphic, despite their apparent similarities.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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