On Flatness and Completion for Infinitely Generated Modules over Noetherian Rings
Amnon Yekutieli
TL;DR
This paper investigates flatness and I-adic completeness of infinitely generated modules over Noetherian rings, introducing concepts like decaying functions and I-adically free modules to address these questions.
Contribution
It introduces new notions such as decaying functions and I-adically free modules to analyze flatness and completeness in the context of infinitely generated modules.
Findings
Characterization of flatness for infinitely generated modules
Conditions for I-adic completeness of modules
Development of the concept of I-adically free modules
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.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models