Abstarct: The study of rings with factorization properties has mainly been focused on integral domains. However, factorization theory in commutative rings with zero divisors is fundamentally different from the domain case and, hence, is an interesting and active area of research. In this thesis, we first recite and scrutinize different notions of associate elements and irreducible elements. This would clarify some fundamental differences between factorization theory in integral domains and commutative rings in general. Then, we review three important classes of rings with factorization properties: ACCP rings, which are rings with ACC on their principal ideals; bounded factorization rings (BFR), which are rings in which the possible lengths of factorizations of a non-zero element into non-units are bounded; and unique factorization rings (UFR), which are defined in a similar way to the integral domain case. For a ring R and an R-module M, the idealization of M in R, which is denoted by R (+) M, is a ring defined on R × M with natural addition, and with the multiplication (r1, ‎x1)(r2‎, ‎x2) = (r1 r2‎, ‎r1 x2‎ + ‎r2 x1). This construction always results in commutative rings with zero-divisors (if M ≠ 0). We show that R (+) M is an ACCP ring if and only if R is ACCP, and M is ACCC (the obvious generalization of ACCP, that is ACC on cyclic R-submodules). We, then, construct a counter-example to show that a similar result does not hold for the bounded factorization property; nevertheless, we show that the bounded factorization property does ascend to R (+) M if we assume a weaker form of the BF property on 0 ∈ R. Finally, we characterize the UFRs resulting from idealization.