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|Title: ||Congruences on monoids of order-preserving or order-reversing transformations on a finite chain|
|Authors: ||Fernandes, Vitor H.|
Gomes, Gracinda M. S.
Jesus, Manuel M.
|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|
|Appears in Collections:||FCT: DM - Artigos em revista internacional com arbitragem científica|
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