CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING TRANSFORMATIONS ON A FINITE CHAIN

CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING TRANSFORMATIONS ON A FINITE CHAIN

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...

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Veröffentlicht in:Glasgow mathematical journal 2005-05, Vol.47 (2), p.413-424
Hauptverfasser: FERNANDES, VÍTOR H., GOMES, GRACINDA M. S., JESUS, MANUEL M.
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GOMES, GRACINDA M. S.
JESUS, MANUEL M.
description 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.
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title CONGRUENCES ON MONOIDS OF ORDER-PRESERVING OR ORDER-REVERSING TRANSFORMATIONS ON A FINITE CHAIN
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