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 is upper semimodular but not lower semimodular.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The second author thanks John Meakin for discussions concerning various aspects of this article. We would also like to express our profound gratitude to the anonymous referee for the valuable remarks and suggestions, which greatly improve the presentation of this article.