Congruences on infinite partition and partial Brauer monoids
MetadataShow full item record
Altmetrics Handle Statistics
We give a complete description of the congruences on the partition monoid PX and the partial Brauer monoid PBX, where X is an arbitrary infinite set, and also of the lattices formed by all such congruences. Our results complement those from a recent article of East, Mitchell, Ruškuc and Torpey, which deals with the finite case. As a consequence of our classification result, we show that the congruence lattices of PX and PBX are isomorphic to each other, and are distributive and well quasi-ordered. We also calculate the smallest number of pairs of partitions required to generate any congruence; when this number is infinite, it depends on the cofinality of certain limit cardinals.
East , J & Ruskuc , N 2021 , ' Congruences on infinite partition and partial Brauer monoids ' , Moscow Mathematical Journal .
Moscow Mathematical Journal
Copyright © 2021 Higher School of Economics, Independent University of Moscow. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://www.mathjournals.org/mmj/.
DescriptionFunding: The first author is supported by ARC Future Fellowship FT190100632. The second author is supported by EPSRC grant EP/S020616/1.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.