Some Properties of Unit, Zero-Divisor and Idempotent Elements of the Ring of Dual Numbers of the Ring Zn, Zn[α]

For any commutative ring with unity R, a new ring can be defined called the ring of dual numbers of the ring R, denoted by R[α]. In this paper we obtain a characterization of unit and zero-divisor elements in the ring of dual numbers of the ring of integers modulo n, Zn[α].