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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An undecidability result for power series rings of positive characteristic
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by Thanases Pheidas PDF
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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Additional 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