  The positive cohomology groups of a finite group acting on a ring vanish when
the ring has a norm-one element. In this note we give explicit homotopies on
the level of cochains when the group is cyclic, which allows us to express any
cocycle of a cyclic group as the coboundary of an explicit cochain. The
formulas in this note are closely related to the effective problems considered
in previous joint work with Eli Aljadeff.
