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Title: On Inverse subsemigroups of the semigroup of orientation preserving or orientation-reversing transformations
Authors: Catarino, Paula
Higgins, Peter
Levi, Inessa
Keywords: semigroup
inverse subsemigroup
strong inverse
order-preserving transformation
orientation-preserving transformation
orientation-reversing transformation
Issue Date: 2015
Publisher: V. Mazorchuk
Citation: Algebra and Discrete Mathematics, 19(2),(2015)162 - 171
Abstract: 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.
Peer Reviewed: yes
ISSN: 1726-3255
Document Type: Article
Appears in Collections:DMAT - Artigo publicado em Revista Científica Indexada

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