Graphs of Commutatively Closed Sets
Rings and Algebras
2021-05-06 v1
Abstract
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively closed subsets of a ring with the help of graph theory. A particular attention is paid to constructions of subsets of a given diameter. In particular, we compute the diameter of artinian semisimple algebras.
Cite
@article{arxiv.2105.02049,
title = {Graphs of Commutatively Closed Sets},
author = {André Leroy and Mona Abdi},
journal= {arXiv preprint arXiv:2105.02049},
year = {2021}
}