Publicação
Classes of semigroups, congruences and languages
| Resumo: | Taking formations of groups and of inverse semigroups as the starting point, formations of orthodox semigroups are defined, as well as the wider class of i-formations (i standing for idempotent-separating). The relation between the nature of classes of inverse semigroups F [of groups G ] and that of certain classes of orthodox semigroups with associated inverse semigroups in F [groups in G ] is discussed. The product of formations of orthodox semigroups, in particular of R-unipotent semigroups, is considered, and a product like the Gaschutz’s known for groups is presented for i-formations. ¨ Further, relations between formations of inverse semigroups, of congruences on inverse semigroups and of congruences on free inverse semigroups are established. Then, i-formations of idempotent separating congruences and of languages are defined on inverse semigroups and their classes are proved to be in bijection, and in bijection with f-formations of inverse semigroups. The concepts of i-Fitting class of inverse semigroups, of congruences and of languages on inverse semigroups are introduced, and bijections between f-Fitting classes of Clifford semigroups, i-Fitting classes of congruences and i-Fitting classes of languages on Clifford semigroups are presented. Of special relevance are results on formations and Fitting classes induced by the inverse case on the group case. Finally, the concepts of i-Fitting-formation of inverse semigroups, congruences and languages on inverse semigrupos are introduced, and bijections between these classes are also establised. This thesis concludes with a list of open questions. |
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| Autores principais: | Monteiro, Ana Catarina Cristino |
| Assunto: | Semigrupo Ortodoxo Semigrupo Inverso Formação Classe de Fitting Quociente que Separa Idempotentes Teses de mestrado - 2024 |
| Ano: | 2024 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | Taking formations of groups and of inverse semigroups as the starting point, formations of orthodox semigroups are defined, as well as the wider class of i-formations (i standing for idempotent-separating). The relation between the nature of classes of inverse semigroups F [of groups G ] and that of certain classes of orthodox semigroups with associated inverse semigroups in F [groups in G ] is discussed. The product of formations of orthodox semigroups, in particular of R-unipotent semigroups, is considered, and a product like the Gaschutz’s known for groups is presented for i-formations. ¨ Further, relations between formations of inverse semigroups, of congruences on inverse semigroups and of congruences on free inverse semigroups are established. Then, i-formations of idempotent separating congruences and of languages are defined on inverse semigroups and their classes are proved to be in bijection, and in bijection with f-formations of inverse semigroups. The concepts of i-Fitting class of inverse semigroups, of congruences and of languages on inverse semigroups are introduced, and bijections between f-Fitting classes of Clifford semigroups, i-Fitting classes of congruences and i-Fitting classes of languages on Clifford semigroups are presented. Of special relevance are results on formations and Fitting classes induced by the inverse case on the group case. Finally, the concepts of i-Fitting-formation of inverse semigroups, congruences and languages on inverse semigrupos are introduced, and bijections between these classes are also establised. This thesis concludes with a list of open questions. |
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