. 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 
.