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TitleBaer-Levi semigroups of linear transformations
Author(s)Gonçalves, Suzana Mendes
Sullivan, R. P.
KeywordsSemigroups of linear transformations
Issue date2004
PublisherRoyal Society of Edinburgh
JournalProceedings of the Royal Society of Edinburgh Section A-Mathematics
Citation“Proceedings section A : mathematics - The Royal Society of Edinburgh”. ISSN 0308-2105. 134:3 (2004) 477-499.
Abstract(s)Given an infinite-dimensional vector space V, we consider the semigroup GS(m,n) of all injective linear transformations of V into itself with defect n, where n is an infinite cardinal less or equal than m, the dimension of V. This is a linear version of the well-known Baer-Levi semigroup BL(p,q) defined on an infinite set X with cardinal p and where q is an infinite cardinal less or equal than p. We show that, although the basic properties of GS(m,n) are the same as those of BL(p,q), the two semigroups are never isomorphic. We also determine all left ideals of GS(m,n) and some of its maximal subsemigroups: in this, we follow previous work on BL(p,q) by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984).
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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