习题 11, § 2

Let $p$ be a prime number, G a group that does not contain any elements of order $p, A$ a commutative ring of characteristic $p$ that does not contain any nonzero nilpotent elements, A[G] the algebra of G over A, and $(e_g)$ the canonical basis of A[G] over A. 证明环 A[G] 不存在非零的零理想（观察如果元素 $\sum a_ge_g\in A[G]$ 幂零的，那么我们有 $a_1= 0$）。