is not closed under multiplication: but .
Showing that is a subring is straightforward. It is not an ideal because and but .
Really struggling with this question.
Let R=C[X] (complex)
S={f(X) = (sum from i=0 to n) a_{i}X^{i} in C[X] : a_{2}= 0} and
T={f(X) = (sum from i=0 to n) a_{i}X^{i} in C[X] : a_{1}= 0}
S and T are the sets of polynomials with coefficients in C and with zero quadratic, respectively linear, term.
Prove that S is not a subring of R
Prove that T is a subring of R, but not an ideal or R.
Any help much appreciated!!