On the core and adjoint of the product of complete ideals in two-dimensional regular local rings

TL;DR

This paper derives formulas for the core and adjoint of the product of complete ideals in two-dimensional regular local rings, using joint reductions, and computes their colengths, extending the Briançon-Skoda theorem.

Contribution

It introduces new expressions for the core and adjoints of ideal products in a specific algebraic setting, generalizing existing theorems.

Findings

Formulas for the core and adjoint of ideal products

Computed colengths of these ideals

Strengthened the Briançon-Skoda theorem generalization

Abstract

Using joint reductions of complete ideals, we find expressions for the core and adjoints of the product of complete ideals in a two-dimensional regular local ring. We also compute their colengths. Our results strengthen a generalization of the Brian\c{c}on-Skoda theorem due to D. Rees and J. D. Sally.