. We will refer to the elements of C by giving them a subscript . The elements of R can be embedded as follows: such that . Furthermore we can define:
There exists an elegant alternative definition using ideals. To be a bit sloppy: , i.e. C is the resulting quotient ring of factoring ideal out of the ring R[x] of polynomials over R. The sloppy part is that we need to define concepts like quotient ring, ideal, and ring of polynomials. Note that this definition is close to working with : can be rewritten as .