§ 1. Introduction. Little is known concerning the theory of resultants of equations other than in the complex number system. The cyclic number systems provide a simple example which is not a division algebra. In such a system with n units er. any number y ≡ y0 + y1e1 + y2e2 + … + yn−1en−1 has coefficients yr drawn from a field, and the units satisfy the product law: