# Math Help - Rings and subrings

1. ## Rings and subrings

Really struggling with this question.

Let R=C[X] (complex)

S={f(X) = (sum from i=0 to n) aiXi in C[X] : a2= 0} and
T={f(X) = (sum from i=0 to n) aiXi in C[X] : a1= 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!!

2. ## Re: Rings and subrings

$S$ is not closed under multiplication: $X\in S$ but $X^2\notin S$.

Showing that $T$ is a subring is straightforward. It is not an ideal because $1\in T$ and $X\in R$ but $1\cdot X\notin T$.