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Title: Congruences on monoids of order-preserving or order-reversing transformations on a finite chain
Authors: Fernandes, Vítor H.
Gomes, Gracinda M. S.
Jesus, Manuel M.
Keywords: Congruences
Issue Date: 2005
Publisher: Cambridge University Press
Abstract: This paper is mainly dedicated to describing the congruences on certain monoids of transformations on a finite chain Xn with n elements. Namely, we consider the monoids ODn and PODn of all full, respectively partial, transformations on Xn that preserve or reverse the order, as well as the submonoid POn of PODn of all its order-preserving elements. The inverse monoid PODIn of all injective elements of PODn is also considered. We show that in POn any congruence is a Rees congruence, but this may not happen in the monoids ODn, PODIn and PODn. However in all these cases the congruences form a chain.
Description: Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424
ISSN: 0017-0895
Appears in Collections:FCT: DM - Artigos em revista internacional com arbitragem científica

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