Vol. 61, No. 1, 1975

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On power-invariance

Eloise A. Hamann

Vol. 61 (1975), No. 1, 153–159

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.

Mathematical Subject Classification 2000
Primary: 13J05
Received: 27 December 1974
Published: 1 November 1975
Eloise A. Hamann