Directed Graphs of Commutative Rings

Authors

Seth Hausken, University of St. ThomasFollow
Jared Skinner, University of St. ThomasFollow

Abstract

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.

Author Bio

Seth Hausken is currently a mathematics student at St Thomas. His interest is mainly in Algebra, especially commutative rings. His future plans are to attend graduate school in mathematics.

Jared Skinner is currently a graduate student at the University of Wyoming. His interests in mathematics are currently of too great a breadth to describe with brevity. Jared intends to be a mathematics professor when finished with his graduate education.

Faculty Sponsor

Mike Axtell

Recommended Citation

Hausken, Seth and Skinner, Jared (2013) "Directed Graphs of Commutative Rings," Rose-Hulman Undergraduate Mathematics Journal: Vol. 14: Iss. 2, Article 11.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss2/11