Prove there exists a left ideal I of C[$\displaystyle S_{3}$] (so the ring in the symmetric group S3 with complex coeffs) which does not contain the element $\displaystyle e_{1}$:= $\displaystyle \frac{1}{6}$ $\displaystyle \sum$ [y] nor the element $\displaystyle e_{2}$:= $\displaystyle \frac{1}{6}$ $\displaystyle \sum$ sgn(y) [y]

(Where both the sums are over all $\displaystyle y$ in $\displaystyle S_{3}$)

(Forgive my Latex; I'm still trying to get the hang of it)