Exercise
In which polynomial ring do we have the equality of ideals ({2, X}) = (2)?
Z/4Z/[X]
Z[X]
Q[X]
No. The element X does not belong to (2), as the latter is the
set of all polynomials with coefficients in {0,2}.
No. The element X does not belong to (2), as the latter is the
set of all polynomials with only even coefficients.
Indeed. In fact, both sides coincide with the ideal R.