Generalized U-factorization in commutative rings with zero-divisors

Abstract

Recently, substantial progress has been made on generalized factorization techniques in integral domains, in particular, $\tau$-factorization. There have 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.