Algebraic Number Theory
《Algebraic Number Theory》 · 第 134 页 · Chapter II，Exercises，Exercises 2–3
Let $A$ be a commutative ring. For $a=(a_0,a_1,\ldots)$, $b=(b_0,b_1,\ldots)$, $a_i,b_i\in A$, put $a+b=(S_0(a,b),S_1(a,b),\ldots)$ and $a\cdot b=(P_0(a,b),P_1(a,b),\ldots)$. Show that with these operations the vectors $a=(a_0,a_1,\ldots)$ form a commutative ring $W(A)$ with $1$. It is called the ring of Witt vectors over $A$.