Congruences on infinite partition and partial Brauer monoids

James East, Nik Ruskuc

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Abstract

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.
Original languageEnglish
JournalMoscow Mathematical Journal
Publication statusAccepted/In press - 9 May 2021

Keywords

  • Diagram monoids
  • Partition monoids
  • Partial Brauer monoids
  • Congruences
  • Well quasi-orderdness

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