Vol. 66, No. 1, 1976

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R-endomorphisms of R[[X]] are essentially continuous

Paul M. Eakin, Jr. and Avinash Madhav Sathaye

Vol. 66 (1976), No. 1, 83–87

Let R be a commutative ring with identity, A = R[[X]] and B = R[[Y ]] with X and Y finite sets of indeterminates. Consider A and B as topological rings with the respective X and Y -adic topologies. If σ : A B is any R-homomorphism then there are R-automorphisms s and t of A and B respectively, so that t σ s : A B is continuous. As a corollary we see that an R-endomorphism of A is surjective only if it is an automorphism.

Mathematical Subject Classification 2000
Primary: 13J05
Received: 28 July 1975
Published: 1 September 1976
Paul M. Eakin, Jr.
Avinash Madhav Sathaye