We extend the notion of a Krull
domain to commutative rings with identity which may contain zero divisors. In order
to do this we present a definition of the divisors of an arbitrary ring, and show that
the collection of divisors is a commutative semigroup with identity and is a group if
and only if the ring is completely integrally closed. In addition, an extension of
unique factorization domains to arbitrary commutative rings is used to investigate
the relationship between Krull rings and unique factorization rings. In particular, it
is shown that a unique factorization ring is a Krull ring with trivial class
group.