Utilize este identificador para referenciar este registo: http://hdl.handle.net/10348/6740
Título: On Inverse subsemigroups of the semigroup of orientation preserving or orientation-reversing transformations
Autor: Catarino, Paula
Higgins, Peter
Levi, Inessa
Palavras-chave: semigroup
semilattice
inverse subsemigroup
strong inverse
transformation
order-preserving transformation
orientation-preserving transformation
orientation-reversing transformation
Data: 2015
Editora: V. Mazorchuk
Citação: Algebra and Discrete Mathematics, 19(2),(2015)162 - 171
Resumo: It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n less than or equal 3.
Revisão por Pares: yes
URI: http://hdl.handle.net/10348/6740
ISSN: 1726-3255
metadata.dc.relation.publisherversion: http://admjournal.luguniv.edu.ua/index.php/adm/article/view/43/10
Tipo de Documento: Artigo
Aparece nas colecções:DMAT - Artigo publicado em Revista Científica Indexada

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