Document type
Journal articles
Document subtype
Full paper
Title
Extensions and covers for semigroups whose idempotents form a left regular band
Participants in the publication
Mário J. J. Branco (Author)
Dep. Matemática
CAUL
Gracinda M. S. Gomes (Author)
Dep. Matemática
CAUL
Victoria Gould (Author)
Summary
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.
Date of Submisson/Request
2009-12-15
Date of Acceptance
2010-03-12
Date of Publication
2010-07-13
Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA
Where published
Semigroup Forum
Publication Identifiers
ISSN - 0037-1912
eISSN - 1432-2137
Publisher
Springer Science and Business Media LLC
Number of pages
20
Starting page
51
Last page
70
Document Identifiers
URL -
http://dx.doi.org/10.1007/s00233-010-9239-9
DOI -
https://doi.org/10.1007/s00233-010-9239-9
Rankings
SCIMAGO Q2 (2009) - 0.855 - Algebra and Number Theory