Orthogonality graphs of matrices over commutative rings
Algebraic Geometry
2022-11-18 v2 Rings and Algebras
Abstract
The paper is devoted to studying the orthogonality graph of the matrix ring over a commutative ring. It is proved that the orthogonality graph of the ring of matrices with size greater than 1 over a commutative ring with zero-divisors is connected and has diameter 3 or 4; a criterion for each value is obtained. It is also shown that each of its vertices has distance at most 2 from some scalar matrix.
Cite
@article{arxiv.2208.03039,
title = {Orthogonality graphs of matrices over commutative rings},
author = {O. G. Styrt},
journal= {arXiv preprint arXiv:2208.03039},
year = {2022}
}