. 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
.