A constructive comparison of the rings R(X) and RX and application to the Lequain–Simis Induction Theorem

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• 作者：Afef Ellouz ; Henri Lombardi ; Ihsen Yengui
• 关键词：Constructive mathematics ; Lequain– ; Simis Induction Theorem ; Quillen– ; Suslin Theorem ; Finitely generated projective modules ; Local– ; global principles ; Prü ; fer domains ; Arithmetical rings
• 刊名：Journal of Algebra
• 出版年：2008
• 出版时间：15 July 2008
• 年：2008
• 卷：320
• 期：2
• 页码：521-533
• 全文大小：160 K

文摘

We constructively prove that for any ring R with Krull dimension d, the ring RX locally behaves like the ring R(X) or a localization of a polynomial ring of type (S⁻¹R)[X] with S a multiplicative subset of R such that the Krull dimension of S⁻¹R is d−1. As an application, we give a simple and constructive proof of the Lequain–Simis Induction Theorem which is an important variation of the Quillen Induction Theorem.