Vol. 51, No. 1, 1974

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Power invariant rings

Joong Ho Kim

Vol. 51 (1974), No. 1, 207–213

A ring A is called power invariant if whenever B is a ring such that the formal power series rings A[[X]] and B[[X]] are isomorphic, then A and B are isomorphic. A ring A is said to be strongly power invariant if whenever B is a ring and ϕ is an isomorphism of A[[X]] onto B[[X]], then there exists a B-automorphism ψ of B[[X]] such that ψ(X) = ϕ(X). Strongly power invariant rings are power invariant. For any commutative ring A,A∕J(A)n is strongly power invariant, where J(A) is the Jacobson radical of A, and n is any positive integer. A left or right Artinian ring is strongly power invariant. If A is a left or right Noetherian ring, then A[t], the polynomial ring in an indeterminate t over A, is strongly power invariant.

Mathematical Subject Classification 2000
Primary: 16A48
Secondary: 13J05
Received: 15 November 1972
Published: 1 March 1974
Joong Ho Kim