  Recently substantial progress has been made on generalized factorization
techniques in integral domains, in particular $\tau$-factorization. There has
also been advances made in investigating factorization in commutative rings
with zero-divisors. One approach which has been found to be very successful is
that of U-factorization introduced by C.R. Fletcher. We seek to synthesize work
done in these two areas by generalizing $\tau$-factorization to rings with
zero-divisors by using the notion of U-factorization.
