On power-invariance

Abstract

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[[]] with Y an analytic indeterminate over S, need S be isomorphic to Rl 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 powerinvariant.