The problem of confounding in the general symmetrical factorial design, s^m, where s is a positive prime integer or power of a prime, has been completely solved by research workers who, for this purpose, utilized the theory of Galois Fields in the set-up of projective geometry. Recently, a mapping technique has been developed by White-Hultquist-Raktoe to provide confounding plans for asymmetrical factorial designs of the type p₁^m₁ × p₂^m₂, where p₁ and p₂ are distinct prime numbers. In this Dissertation, new Lemmas and Theorems have been proven to extend the results obtained by White-Hultquist-Raktoe to include the combination of finite rings of integers which are not necessarily prime, but are relatively prime. This generalization has all the desirable properties of confounding, and covers a much wider class of mixed factorial experiments, where the numbers of levels of factors are not all primes. Examples have also been provided in support of results proven in this Dissertation.