Tipo
Documentos Académicos
Tipo de Documento
Tese de Doutoramento
Título
Aspects of order and congruence relations on regular semigroups
Participantes na publicação
Gracinda M. S. Gomes (Author)
Dep. Matemática
CEMAT
Resumo
On a regular semigroup S natural order relations have been defined by Nambooripad and by Lallement. Different characterisations and relationships between the Nambooripad order J, Lallement's order λ and a certain relation k are considered in Chapter I. It is shown that on a regular semigroup S the partial order J is left compatible if and only if S is locally R-unipotent. This condition in the case where S is orthodox is equivalent to saying that E(S) is a left seminormal band. It is also proved that λ is the least compatible partial order contained in J and that k = λ if and only if k is compatible and k if and only if J is compatible. A description of λ and J in the semigroups T(X) and PT(X) is presented. In Chapter II, it is proved that in an orthodox semigroup S the band of idempotents E(S) is left quasinormal if and only if there exists a local isomorphism from S onto an R-unipotent semigroup. It is shown that there exists a least R-unipotent congruence on any orthodox semigroup, generated by a certain left compatible equivalence R. This equivalence is a congruence if and only if E(S) is a right semiregular band. The last Chapter is particularly concerned with the description of R-unipotent congruences on a regular semigroup S by means of their kernels and traces. The lattice RC(S) of all R-unipotent congruences on a regular semigroup S is studied. A congruence≡ on the lattice RC(S) is considered and the greatest and the least element of each ≡-class are described.
Instituição
UNIVERSIDADE DE ST. ANDREWS
Identificadores da Publicação
Editora
University of St. Andrews