Article ID Journal Published Year Pages File Type
9497515 Journal of Pure and Applied Algebra 2005 21 Pages PDF
Abstract
In (J. Symbolic Logic 56(2) (1991) 539), Bélair developed a theory analogous to the theory of real closed rings in the p-adic context, namely the theory of p-adically closed integral rings. Firstly we use the property proved in Lemma 2.4 in (J. Symbolic Logic 60(2) (1995) 484) to express this theory in a language including a p-adic divisibility relation and we show that this theory admits definable Skolem functions in this language (in the sense of (J. Symbolic Logic 49 (1984) 625)). Secondly, we are interested in dealing with some questions similar to that of (Z. Math. Logik Grundlag. 29(5) (1983) 417); e.g., results about integral-definite polynomials over a p-adically closed integral ring A and a kind of “Nullstellensatz” using the notion of MA-radical.
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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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