Soit \(E = K_3[X]\), \(F = \{ P \in E\) tq \(P(0) = P(1) = P(2) = 0 \}\), \(G = \{ P \in E\) tq \(P(1) = P(2) = P(3) = 0 \}\), et \(H = \{ P \in E\) tq \(P(X) = P(-X) \}\).
1
Montrer que \(F \oplus G = \{ P \in E\) tq \(P(1) = P(2) = 0 \}\).
2
Montrer que \(F \oplus G \oplus H = E\).