Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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An undecidability result for power series rings of positive characteristic
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by Thanases Pheidas
Proc. Amer. Math. Soc. 99 (1987), 364-366
DOI: https://doi.org/10.1090/S0002-9939-1987-0870802-X
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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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Bibliographic Information
  • © Copyright 1987 American Mathematical Society
  • 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