Integral dimension of a noetherian ring
Caijun Zhou
TL;DR
This paper introduces the integral dimension, a new invariant for noetherian rings, which generalizes the weak Briancon-Skoda numbers and is finite for all noetherian local rings.
Contribution
It defines the integral dimension for noetherian rings and establishes its finiteness for all noetherian local rings, extending the understanding of ring invariants.
Findings
Integral dimension is a well-defined invariant for noetherian rings.
Every noetherian local ring has finite integral dimension.
The integral dimension generalizes the weak Briancon-Skoda numbers.
Abstract
In this paper, we introduce a new notion, called the integral dimension, for noetherian rings. It can be regarded as the weak Briancon-Skoda numbers of rings. The point is that every noetherian local ring has finite integral dimension.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models