An alternative to Witt vectors

The ring of Witt vectors associated to a ring R is a classical tool in algebra. We introduce a ring C® which is more easily constructed and which is isomorphic to the ring of Witt vectors W® for a perfect F_p-algebra R. It is obtained as the completion of the monoid ring ZR, for the multiplicative monoid R, with respect to the powers of the kernel of the natural map from ZR to R.