On Flatness and Completion for Infinitely Generated Modules over Noetherian Rings

2009/02/25 by Amnon Yekutieli, Yekutieli, Amnon
Mathematics · #13C10 #13C11 (Secondary) #13E05 #13J10 (Primary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13C10 #msc:13C11 #msc:13E05 #msc:13J10

paper · pdf · doi:10.48550/arxiv.0902.4378

Minor improvements. Final version, to appear in Comm. Algebra

arxiv created 2010/02/12 · arxiv updated 2010/02/26

Abstract

Let A be a noetherian commutative ring, and let I be an ideal in A. We study questions of flatness and I-adic completeness for infinitely generated A-modules. This is done using the notions of decaying function and I-adically free A-module.

Related

• Flatness and Completion Revisited
• Detecting completeness from ext-vanishing
• A new proof of the local criterion of flatness
• Notes on finitely generated flat modules
• On Preservation Properties and a Special Algebraic Characterization of Some Stronger Forms of the Noetherian Condition