Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/16882
Título: | Inverse semigroups generated by nilpotent transformations |
Autor(es): | Howie, John M. Smith, M. Paula Marques |
Palavras-chave: | Inverse semigroup Nilpotents Transformations Congruences |
Data: | 1984 |
Editora: | Cambridge University Press |
Revista: | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Resumo(s): | Let $X$ be a set with infinite cardinality $m$ and let $B$ be the Baer-Levi semigroup, consisting of all one-one mappings $a:X\rightarrow X$ for which $∣X\Xα∣ = m$. Let $K_m=<B^{-1}B>$, the inverse subsemigroup of the symmetric inverse semigroup $\mathcal T(X)$ generated by all products $\beta^{−1}\gamma$, with $\beta,1\gamma\in B$. Then $K_m = <N_2>$, where $N_2$ is the subset of $\mathcal T(X)$ consisting of all nilpotent elements of index 2. Moreover, $K_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2\subset K_m = N_2\cup N_2^2\cup N_2^3$. Let $P_m$ be the ideal $\{\alpha\in K_m: ∣dom \alpha∣<m\}$ in $K_m$ and let $L_m$ be the Rees quotient $K_m/P_m$. Then $L_m$ is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image $L_m^*$ of $L_m$ also has these properties and is congruence-free. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/16882 |
DOI: | 10.1017/S0308210500026032 |
ISSN: | 0308-2105 |
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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Inv_sgps_nilpo_transf.pdf | 2,68 MB | Adobe PDF | Ver/Abrir |