On Inverse subsemigroups of the semigroup of orientation preserving or orientation-reversing transformations
Data
2015
Autores
Título da revista
ISSN da revista
Título do Volume
Editora
V. Mazorchuk
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.
Descrição
Palavras-chave
semigroup , semilattice , inverse subsemigroup , strong inverse , transformation , order-preserving transformation , orientation-preserving transformation , orientation-reversing transformation
Citação
Algebra and Discrete Mathematics, 19(2),(2015)162 - 171