An undecidability result for power series rings of positive characteristic
Author:
Thanases Pheidas
Journal:
Proc. Amer. Math. Soc. 99 (1987), 364-366
MSC:
Primary 03D35; Secondary 12L05, 13L05
DOI:
https://doi.org/10.1090/S0002-9939-1987-0870802-X
MathSciNet review:
870802
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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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Article copyright:
© Copyright 1987
American Mathematical Society
