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|Title:||On Inverse subsemigroups of the semigroup of orientation preserving or orientation-reversing transformations|
|Citation:||Algebra and Discrete Mathematics, 19(2),(2015)162 - 171|
|Abstract:||It is well-known  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.|
|Appears in Collections:||DMAT - Artigo publicado em Revista Científica Indexada|
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