An algebraic proof of the commutativity of the intersection with divisors

TL;DR

This paper provides an algebraic proof demonstrating that intersecting with divisors on the Chow group of a local Noetherian domain is commutative, offering a new perspective on this fundamental property.

Contribution

It introduces a purely algebraic proof of the commutativity of divisor intersection on the Chow group, avoiding geometric or topological methods.

Findings

Proof confirms intersection with divisors is commutative in this setting

Establishes algebraic approach as viable alternative to geometric proofs

Enhances understanding of Chow groups in algebraic geometry

Abstract

We present a purely algebraic proof of the commutativity of the operation defined by intersection with divisors on the Chow group of a local Noetherian domain.