Distributivity in congruence lattices of graph inverse semigroups
Group Theory
2023-03-29 v1
Abstract
Let {\Gamma} be a directed graph and Inv({\Gamma}) be the graph inverse semigroup of {\Gamma}. Luo and Wang [7] showed that the congruence lattice C(Inv({\Gamma})) of any graph inverse semigroup Inv({\Gamma}) is upper semimodular, but not lower semimodular in general. Anagnostopoulou-Merkouri, Mesyan and Mitchell characterized the directed graph {\Gamma} for which C(Inv({\Gamma})) is lower semimodular [2]. In the present paper, we show that the lower semimodularity, modularity and distributivity in the congruence lattice C(Inv({\Gamma})) of any graph inverse semigroup Inv({\Gamma}) are equivalent.
Keywords
Cite
@article{arxiv.2303.15797,
title = {Distributivity in congruence lattices of graph inverse semigroups},
author = {Yongle Luo and Zhengpan Wang and Jiaqun Wei},
journal= {arXiv preprint arXiv:2303.15797},
year = {2023}
}
Comments
11 pages, 3 figures