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Abstract

The directed graph of a ring is a graphical representation of its additive and multiplicative structure. Using the directed edge relationship (a,b) → (a+b,a ⋅ b), one can create a directed graph for every ring. This paper focuses on the structure of the sources in directed graphs of commutative rings with identity, with special concentration in the finite and reduced cases.

Author Bio

Christopher Ang graduated from University of St. Thomas in the Spring of 2012 with a B.A. in Pure Mathematics. He has just finished his first year of graduate study in the doctoral program at Michigan State University. He hopes to be a professor of mathematics at a university. He collaborated with Alex Schulte in the research for this paper under the supervision of Dr. Michael Axtell at the University of St. Thomas during the summer of 2012.

Alex Schulte will graduate from the University of St. Thomas in the Spring of 2013 with a B.A. in Pure Mathematics. He hopes to continue his education and obtain a Ph.D. in Mathematics. He then wishes to become a professor at the college level. He collaborated with Christopher Ang in the research for this paper under the supervision of Dr. Michael Axtell at the University of St. Thomas during the summer of 2012.

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