Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/14500
Título: | Associate subgroups of orthodox semigroups |
Autor(es): | Blyth, T. S. Giraldes, E. Smith, M. Paula Marques |
Palavras-chave: | Orthodox semigroup Regular monoid Medial idempotent Associate elements |
Data: | 1994 |
Editora: | Oxford University Press |
Revista: | Glasgow Mathematical Journal |
Resumo(s): | A unit regular semigroup [1, 4] is a regular monoid S such that H1 intersection A(x) ≠ Ø for every element x of S, where H1, is the group of units and A(x) = {y in S; xyx = x} is the set of associates (or pre-inverses) of x. A uniquely unit regular semigroupis a regular monoid 5 such that |H1 intersection A(x)| = 1. Here we shall consider a more general situation. Specifically, we consider a regular semigroup S and a subsemigroup T with the property that |T intersection A(x) = 1 for every x in S. We show that T is necessarily a maximal subgroup Hα for some idempotent α. When Sis orthodox, α is necessarily medial (in the sense that x = xαx for every x, product of idempotents) and αSα is uniquely unit orthodox. When S is orthodox and α is a middle unit (in the sense that xαy = xy for all x, y in S), we obtain a structure theorem which generalises the description given in [2] for uniquely unit orthodox semigroups in terms of a semi-direct product of a band with a identity and a group. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/14500 |
DOI: | 10.1017/S0017089500030706 |
ISSN: | 0017-0895 |
Versão da editora: | http://journals.cambridge.org |
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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Asso_subg.pdf | 2,83 MB | Adobe PDF | Ver/Abrir |