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TitleInjective linear transformations with equal gap and defect
Author(s)Araújo, C. Mendes
Gonçalves, Suzana Mendes
Green's relations
Injective linear transformations
Issue dateFeb-2022
PublisherCambridge University Press
JournalBulletin of the Australian Mathematical Society
CitationMendes Araújo, C., & Mendes-Gonçalves, S. (2022). Injective linear transformations with equal gap and defect. Bulletin of the Australian Mathematical Society, 105(1), 106-116. doi:10.1017/S0004972721000344
Abstract(s)Suppose V is an infinite-dimensional vector space over a field F and let I(V) denote the inverse semigroup of all injective partial linear transformations on V. Given ß in I(V), we denote the domain and the range of ß by dom ß and im ß, respectively, and we call the cardinals g(ß)=codim(domß) and d(ß)=codim(imß) the `gap' and the `defect' of ß, respectively. In this paper, we study the semigroup A(V) of all injective partial linear transformations with equal gap and defect, and characterise Green's relations and ideals in A(V). This is analogous to work by Sanwong and Sullivan in 2009 on a similarly-defined semigroup for the set case, but we show that these semigroups are never isomorphic.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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