Suppose R is an Abstract Witt
Ring in the terminology of Knebusch, Rosenberg, and Ware so R =Z[G]∕K where G
is Abelian and p-primary. Suppose further that G has exponent p and that, for all
x ∈ Z[G], x ∈ K implies xp∕p ∈ K. For example, this holds in the case where p = 2
and R is strongly representational. Let M= M∕K be the fundamental ideal of R.
Then a system of divided powers is defined on the torsion part of M and there is a
well-behaved exponential map defined on the torsion part of M2. This yields a
description of the multiplicative group of units of R in terms of the additive structure
of M2.
