BIBLIOS

Tipo
Artigos em Revista

Tipo de Documento
Artigo Completo

Título
Extensions and covers for semigroups whose idempotents form a left regular band

Participantes na publicação
Mário J. J. Branco (Author)
Dep. Matemática
CAUL
Gracinda M. S. Gomes (Author)
Dep. Matemática
CAUL
Victoria Gould (Author)

Resumo
Proper extensions that are “injective on L-related idempotents” of R-unipotent  semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a lambda-semidirect product of a left regular band by an R-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion. \nAs a consequence of our embedding, we are able to give a structure theorem for proper left restriction semigroups. Further, we show that any glrac semigroup S has a proper cover that is a semidirect product of a left regular band by a monoid, and if S is left restriction, the left regular band may be taken to be a semilattice.


Instituição
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Suporte
Semigroup Forum

Identificadores da Publicação
ISSN - 0037-1912
eISSN - 1432-2137

Editora
Springer Science and Business Media LLC



Identificadores do Documento
URL - http://dx.doi.org/10.1007/s00233-010-9239-9
DOI - https://doi.org/10.1007/s00233-010-9239-9

Identificadores de Qualidade
SCIMAGO Q2 (2009) - 0.855 - Algebra and Number Theory