• Corpus ID: 248563056

Properties of Congruence Lattices of Graph Inverse Semigroups

  title={Properties of Congruence Lattices of Graph Inverse Semigroups},
  author={Marina Anagnostopoulou-Merkouri and Zachary Mesyan and J. D. Mitchell},
From any directed graph E one can construct the graph inverse semigroup G ( E ), whose elements, roughly speaking, correspond to paths in E . Wang and Luo showed that the congruence lattice L ( G ( E )) of G ( E ) is upper-semimodular for every graph E , but can fail to be lower-semimodular for some E . We provide a simple characterisation of the graphs E for which L ( G ( E )) is lower-semimodular. We also describe those E such that L ( G ( E )) is atomistic, and characterise the minimal… 



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  • Aug. 2022. doi: 10.5281/zenodo.592893. url: http://dx.doi.org/10.5281/zenodo.592893
  • 2022

Moreover, if (H, W, f ) is the join of finitely many atoms, then H has finitely many strongly