Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2006, January 21.

Abstract:
The main goal of this paper is to introduce and to study the notion of $p$-adic ring by analogy of the real case (\emph{see} \cite{Ct}). This allows us to generalize the notion of $p$-adic ideal (\emph{see} \cite{Sr}) for any commutative ring with unit. We use after that those notions to give a new characterization of the points of the $p$-adic spectrum of a ring, and a prove of the Nullstellensatz of this spectrum.

Mathematics Subject Classification (2000): 12J12; 14Pxx; 13F20.

Keywords and Phrases: Idéal $p$-adique, spectre $p$-adique, théorème des zéros $p$-adiques.

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