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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870802-X
PII: S 0002-9939(1987)0870802-X
Article copyright: © Copyright 1987 American Mathematical Society