Directed Graphs of Commutative Rings with Identity
Speakers: Chris Ang and Alex Schulte, UST
Date & Time:
7:00 AM - 8:00 AM
Abstract: The directed graph (digraph) of a commutative ring is a graphical representation of its additive and multiplicative structure. Using the directed edge relationship (a, b) points to (a+b, ab) one can create a directed graph for every commutative ring. One important concept in our research is an incoming degree. The incoming degree of a vertex is the number of other vertices that point to it. When no other vertices point to a vertex we call it a source. Throughout our research we focused on determining the sources of different digraphs. We found an interesting result linking the sources in the digraph of a factor ring, and the sources in the digraph of the ring. Later in our research, we examined the digraphs of reduced rings. Probably the best result we got from this was finding we can determine if a ring is reduced or not simply by looking at its digraph. This result can be used even if the digraph is unlabeled.