Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/79996

TitleInjective linear transformations with equal gap and defect
Author(s)Araújo, C. Mendes
Gonçalves, Suzana Mendes
Keywordsideals
Green's relations
Injective linear transformations
Quasiresiduals
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.
TypeArticle
URIhttps://hdl.handle.net/1822/79996
DOI10.1017/S0004972721000344
ISSN0004-9727
e-ISSN1755-1633
Publisher versionhttps://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/abs/injective-linear-transformations-with-equal-gap-and-defect/7B274AACAF3E385DE84825B5A0532BA7
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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