Numerical characterizations for integral dependence of graded modules

TL;DR

This paper introduces new numerical functions to analyze integral dependence of graded modules, providing simple criteria based on invariants in a graded algebraic setting.

Contribution

It develops adic, saturated, and epsilon-density functions for torsion-free modules and applies them to establish criteria for integral dependence in graded modules.

Findings

Introduces adic, saturated, and epsilon-density functions for graded modules.

Provides criteria for checking integral dependence using these functions.

Connects invariants with integral dependence in a graded context.

Abstract

In this paper we construct {\em adic}, {\em saturated} and $\varepsilon$-density functions for a torsion-free module in a graded setup. Then we give some simple criteria for checking the integral dependence of two graded modules $N\subseteq M$ in terms of various well-studied invariants.