Projects per year
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
Fingerprint
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
Ruskuc, N. (PI)
15/12/18 → 14/02/21
Project: Standard