# Properties of Congruence Lattices of Graph Inverse Semigroups

@inproceedings{AnagnostopoulouMerkouri2021PropertiesOC, title={Properties of Congruence Lattices of Graph Inverse Semigroups}, author={Marina Anagnostopoulou-Merkouri and Zachary Mesyan and J. D. Mitchell}, year={2021} }

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…

## Figures from this paper

## References

SHOWING 1-10 OF 19 REFERENCES

### Semimodularity in congruence lattices of graph inverse semigroups

- Mathematics
- 2021

Abstract Congruences on a graph inverse semigroup were recently described in terms of the underline graph. Based on such descriptions, we show that the congruence lattice of a graph inverse semigroup…

### Inverse semigroups on graphs

- Mathematics
- 1975

For each [directed] graph we construct an inverse semigroup. Our main application is a simple proof of the characterization of partially ordered sets ofJ-classes of finite semigroups, and some…

### The lattice of congruences on an inverse semigroup.

- Mathematics
- 1975

1* Introduction. Inverse semigroup congruences were first studied in terms of kernel normal systems. Preston [11] defined a kernel normal system over an inverse semigroup S to be any collection of…

### Leavitt Path Algebras

- Mathematics
- 2017

The central concept of this thesis is that of Leavitt path algebras, a notion introduced by both Abrams and Aranda Pino in [AA1] and Ara, Moreno and Pardo in [AMP] in 2004. The idea of using a field…

### The structure of a graph inverse semigroup

- Mathematics
- 2014

Given any directed graph E one can construct a graph inverse semigroupG(E), where, roughly speaking, elements correspond to paths in the graph. In this paper we study the semigroup-theoretic…

### GRAPH INVERSE SEMIGROUPS, GROUPOIDS AND THEIR C -ALGEBRAS

- Mathematics
- 2002

We develop a theory of graph C -algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a…

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

### Semigroups - GAP package, Version 5.0.2

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