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##
A dynamical comparison between the rings R⟨X⟩ and R(X)

pdf file.

Afef Ellouz, Henri Lombardi and Ihsen Yengui

J. Algebra **320 **, (2008), 521-533.
** Abstract :**

We prove that for any ring
R with Krull dimension ≤ k, the localization
of R[X] at monic polynomials (denoted by R⟨X⟩)
"dynamically behaves" like the
ring R(X) (i.e. the localization
of R[X] at primitive polynomials) or a localization of a polynomial
ring of type R_{S}[X]
where S is a multiplicatively closed subset of R with dim(R_{S}) ≤ k-1.

As application, we give a simple and constructive
proof of Lequain-Simis Theorem which is an important variation
of the Quillen-Suslin Theorem. Our proof is based on a contructive
variant of the Lequain-Simis Induction.