An undecidability result for power series rings of positive characteristic

Pheidas, Thanases

doi:10.1090/S0002-9939-1987-0870802-X

An undecidability result for power series rings of positive characteristic
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Proc. Amer. Math. Soc. 99 (1987), 364-366 Request permission

Abstract:

We prove that the existential theory of a power series ring in one variable over an integral domain $F$ of positive characteristic, with cross section, is undecidable whenever $F$ does not contain an $e$ such that ${e^p} - e = 1$. For example, the result is valid if $F = {Z_p}$ (the $p$-element field where $p$ is a prime).

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