# Commutative rings

## Homework Statement

Show that a finite commutative ring with no zero divisors is an integral domain (i.e. contains a unity element)

## Homework Equations

If a,b are elements in a ring R, then ab=0 if and only if either a and b are 0.

## The Attempt at a Solution

I've been trying to use the cancellation laws.

Dick
Homework Helper
Let N be the set of all nonzero elements of the ring R. Pick a nonzero element c. Can you show cN=N? Remember N is a finite set.

Dick