Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/16144
Título: | The ideal structure of semigroups of linear transformations with lower bounds on their nullity or defect |
Autor(es): | Gonçalves, Suzana Mendes Sullivan, R. P. |
Palavras-chave: | Bi-ideal Quasi-ideal Linear transformation semigroup Maximal regular subsemigroup Maximal right cancellative subsemigroup |
Data: | Mar-2010 |
Editora: | World Scientific and Engineering Academy and Society (WSEAS) |
Revista: | Algebra Colloquium |
Resumo(s): | Suppose V is an infinite-dimensional vector space and let T(V ) denote the semigroup (under composition) of all linear transformations of V . In this paper, we study the semigroup OM(p, q) consisting of all alpha in T(V ) for which dim ker >= q and the semigroup OE(p, q) of all alpha in T(V ) for which codim ran >= q, where dim V = p >= q >= aleph0. It is not difficult to see that OM(p, q) and OE(p, q) are a right and a left ideal of T(V ), respectively, and using these facts we show that they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Also, we describe the Green’s relations and the two-sided ideals of each semigroup, and we determine its maximal regular subsemigroup. Finally, we determine some maximal right cancellative subsemigroups of OE(p, q). |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/16144 |
DOI: | 10.1142/S1005386710000131 |
ISSN: | 1005-3867 |
Versão da editora: | http://www.worldscinet.com/ac/17/1701/S10053867101701.html |
Arbitragem científica: | yes |
Acesso: | Acesso restrito UMinho |
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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lower_bounds.pdf Acesso restrito! | Documento principal | 200,31 kB | Adobe PDF | Ver/Abrir |