Abstract
The purpose of this note is to prove that a Dedekind domain R which contains a field k, and which is a subring ofk[x 1,…,x n ] is a ring of polynomials. This generalizes similar results of A. Evyatar and A. Zaks on principal ideal domains, and of P. M. Cohn for the casen=1. Our methods and proofs differ from those introduced previously.
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References
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This research was partially supported by the National Science Foundation, Grant GP-23861.
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Zaks, A. Dedekind subrings ofk[x 1,…,x n ] are rings of polynomials. Israel J. Math. 9, 285–289 (1971). https://doi.org/10.1007/BF02771678
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DOI: https://doi.org/10.1007/BF02771678