Flat maps to and from Noetherian rings
Justin Chen
TL;DR
This paper studies flat ring maps involving Noetherian rings, establishing conditions for their existence, and introduces new examples including a novel class of zero-dimensional local rings.
Contribution
It provides necessary and sufficient conditions for flat maps with Noetherian rings and introduces a new class of zero-dimensional local rings.
Findings
Derived conditions for flat maps involving Noetherian rings.
Developed general properties of flat ring maps.
Presented new examples, including a zero-dimensional local ring class.
Abstract
We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many examples, including a new class of zero-dimensional local rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory