Geodesic
CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING TRANSFORMATIONS ON A FINITE CHAIN
Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 413-424

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This paper is mainly dedicated to describing the congruences on certain monoids of transformations on a finite chain $X_n$ with $n$ elements. Namely, we consider the monoids $\od_n$ and $\mpod_n$ of all full, respectively partial, transformations on $X_n$ that preserve or reverse the order, as well as the submonoid $\po_n$ of $\mpod_n$ of all its order-preserving elements. The inverse monoid $\podi_n$ of all injective elements of $\mpod_n$ is also considered.We show that in $\po_n$ any congruence is a Rees congruence, but this may not happen in the monoids $\od_n$, $\podi_n$ and $\mpod_n$. However in all these cases the congruences form a chain.
DOI : 10.1017/S0017089505002648
Mots-clés : 20M20, 20M05, 20M17 
FERNANDES, VÍTOR H.; GOMES, GRACINDA M. S.; JESUS, MANUEL M. CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING TRANSFORMATIONS ON A FINITE CHAIN. Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 413-424. doi: 10.1017/S0017089505002648
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     title = {CONGRUENCES {ON} {MONOIDS} {OF} {ORDER-PRESERVING} {OR} {ORDER-REVERSING} {TRANSFORMATIONS} {ON} {A} {FINITE} {CHAIN}},
     journal = {Glasgow mathematical journal},
     pages = {413--424},
     year = {2005},
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     doi = {10.1017/S0017089505002648},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002648/}
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