Abstract: In this talk we will consider the zero divisor graph of a commutative ring with identity. This is a topic that much literature has been devoted to in the past decade or so and is of much interest (and also has the advantage of being pretty accessible).

A zero divisor in a commutative ring is an element x such that there is a nonzero y with xy=0 (for example, the elements 0,2,3,4 are all zero divisors in the ring Z/6Z). Other familiar examples of zero divisors include many continuous functions (or for you Math 128/129 fans, matrices, but the ring here is not commutative).

The idea behind a zero divisor graph is to give a "graphical" or visual representation of the structure of zero divisors in a commutative ring. One takes the set of nonzero sero divisors as the set of vertices and then you connect the vertices x and y if and only if xy=0. The types of graphs that correspond to zero divisor graphs of commutative rings are not completely understood, but there are many nice things that are know and we will look at some of these this Friday.

Do not worry if you have not heard some of this terminology (zero divisor, ring, graph). The talk will be self-contained and should be accessible to all (so bring your friends)!!