$\mathbb{Z}R$ and rings of Witt vectors $W_S(R)$

Abstract

Using $\lambda$ operations, we give some results on the kernel of the natural map from the monoid algebra $\mathbb{Z}R$ of a commutative ring $R$ to the ring of $S$-Witt vectors of $R$. As a byproduct we obtain a very natural interpretation of a power series used by Dwork in his proof of the rationality of zeta functions for varieties over finite fields.