Properties of congruence lattices of graph inverse semigroups

Marina Anagnostopoulou-Merkouri; Zachary Mesyan; James D. Mitchell

doi:10.1142/S0218196724500139

Properties of congruence lattices of graph inverse semigroups

Marina Anagnostopoulou-Merkouri, Zachary Mesyan^*, James D. Mitchell

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 characterization 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 characterize the minimal generating sets for L(G(E)) when E is finite and simple.

Original language	English
Pages (from-to)	371-396
Number of pages	26
Journal	International Journal of Algebra and Computation
Volume	34
Issue number	3
Early online date	20 Apr 2024
DOIs	https://doi.org/10.1142/S0218196724500139
Publication status	Published - 1 May 2024

Keywords

Inverse semigroup
Directed graph
Congruence lattice
Semimodular
Atomistic

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10.1142/S0218196724500139

Anagnostopoulou-Merkouri_2024_IJoAaC_Properties-congruence-lattices-semigroups_AAM
Copyright © 2024 Publisher / the Author(s). This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1142/S0218196724500139
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abstract = "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 characterization 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 characterize the minimal generating sets for L(G(E)) when E is finite and simple.",

keywords = "Inverse semigroup, Directed graph, Congruence lattice, Semimodular, Atomistic",

author = "Marina Anagnostopoulou-Merkouri and Zachary Mesyan and Mitchell, \{James D.\}",

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AU - Anagnostopoulou-Merkouri, Marina

AU - Mesyan, Zachary

AU - Mitchell, James D.

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Y1 - 2024/5/1

N2 - 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 characterization 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 characterize the minimal generating sets for L(G(E)) when E is finite and simple.

AB - 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 characterization 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 characterize the minimal generating sets for L(G(E)) when E is finite and simple.

KW - Inverse semigroup

KW - Directed graph

KW - Congruence lattice

KW - Semimodular

KW - Atomistic

UR - https://www.scopus.com/pages/publications/85191387785

U2 - 10.1142/S0218196724500139

DO - 10.1142/S0218196724500139

M3 - Article

AN - SCOPUS:85191387785

SN - 0218-1967

VL - 34

SP - 371

EP - 396

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 3

ER -

Properties of congruence lattices of graph inverse semigroups

Abstract

Keywords

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