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Abstract
We give a complete description of the congruences on the partition monoid P_{X} and the partial Brauer monoid PB_{X}, 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 P_{X} and PB_{X} are isomorphic to each other, and are distributive and well quasiordered. 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 language  English 

Journal  Moscow Mathematical Journal 
Publication status  Accepted/In press  9 May 2021 
Keywords
 Diagram monoids
 Partition monoids
 Partial Brauer monoids
 Congruences
 Well quasiorderdness
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Dive into the research topics of 'Congruences on infinite partition and partial Brauer monoids'. Together they form a unique fingerprint.Projects
 1 Finished

Diagram Monoids and Their Congruences: Diagram Monoids and Their Congruences
15/12/18 → 14/02/21
Project: Standard