The directed graph of a commutative ring is a graph representation of its additive and multiplicative structure. Using the mapping (a,b) → (a+b,a ⋅ b) one can create a directed graph for every finite, commutative ring. We examine the properties of directed graphs of commutative rings, with emphasis on the information the graph gives about the ring.
Prof. Mike Axtell, Department of Mathematics, University of St. Thomas
Hausken, Seth and Skinner, Jared
"Directed Graphs of Commutative Rings,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 11.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss2/11