Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Fernandes, Vítor H.; Gomes, Gracinda M. S.; Jesus, Manuel M.

http://hdl.handle.net/10362/5322

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Autores

Fernandes, Vítor H.

Gomes, Gracinda M. S.

Jesus, Manuel M.

Resumo(s)

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.

Descrição

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Palavras-chave

Congruences Order-preserving Order-reversing Transformations

URI

http://hdl.handle.net/10362/5322

Editora

Cambridge University Press

Coleções

FCT: DM - Artigos em revista internacional com arbitragem científica

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