Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/79996
Título: | Injective linear transformations with equal gap and defect |
Autor(es): | Araújo, C. Mendes Gonçalves, Suzana Mendes |
Palavras-chave: | ideals Green's relations Injective linear transformations Quasiresiduals |
Data: | Fev-2022 |
Editora: | Cambridge University Press |
Revista: | Bulletin of the Australian Mathematical Society |
Citação: | Mendes 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 |
Resumo(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. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/79996 |
DOI: | 10.1017/S0004972721000344 |
ISSN: | 0004-9727 |
e-ISSN: | 1755-1633 |
Versão da editora: | https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/abs/injective-linear-transformations-with-equal-gap-and-defect/7B274AACAF3E385DE84825B5A0532BA7 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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Injective_linear_transformations_equal_gap_defect.pdf | Injective linear transformations with equal gap and defect | 181,41 kB | Adobe PDF | Ver/Abrir |