Graphs of commutatively closed sets
Mona Abdi, André Leroy
Abstract
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of some associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively closed subsets of a ring with the help of graph theory. In particular, we compute the diameter of matrix rings and Artinian semisimple algebras.
Topics & Concepts
MathematicsAlgebraic propertiesGraphAlgebraic numberDiscrete mathematicsAlgebra over a fieldCombinatoricsPure mathematicsMathematical analysisRings, Modules, and AlgebrasAdvanced Topics in AlgebraAlgebraic structures and combinatorial models