Congruences on infinite partition and partial Brauer monoids
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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
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DescriptionFunding: The first author is supported by ARC Future Fellowship FT190100632. The second author is supported by EPSRC grant EP/S020616/1.
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