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Proceedings of the American Mathematical Society

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

 
 

 

Decidable sentences over polynomial rings


Author: Shih Ping Tung
Journal: Proc. Amer. Math. Soc. 102 (1988), 383-388
MSC: Primary 03B25,; Secondary 03C60,12L05
DOI: https://doi.org/10.1090/S0002-9939-1988-0921004-0
MathSciNet review: 921004
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Abstract: Let $ R$ be an algebraic number field or an algebraic integer ring. We prove that there is an algorithm to determine whether the sentence $ \forall x\exists y\phi \left( {x,y} \right)$, with $ \phi \left( {x,y} \right)$ a quantifier free formula over $ R\left[ T \right]$, is true in the polynomial ring $ R\left[ T \right]$ or not.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0921004-0
Article copyright: © Copyright 1988 American Mathematical Society

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