Let R be a commutative ring
with identity, and consider the power series ring R[[X]] in one analytic indeterminate
over R. Is the coefficient ring R unique in the sence that if R[[X]] is isomorphic
to S[[Y ]] with Y an analytic indeterminate over S, need S be isomorphic
to R? Whenever this is the case, R will be called power-invariant. It will
be shown that if R is a quasi-local or a complete semi-local ring then R is
power-invariant.