# Little dimension and the improved new intersection theorem

## TL;DR

This paper introduces the little dimension, a new invariant for modules over commutative noetherian local rings, and uses it to extend the improved new intersection theorem, advancing understanding in commutative algebra.

## Contribution

The paper defines the little dimension and applies it to generalize the improved new intersection theorem in commutative algebra.

## Key findings

- Introduction of the little dimension invariant.
- Extension of the improved new intersection theorem.
- Potential applications to module theory.

## Abstract

Let $R$ be a commutative noetherian local ring. We define a new invariant for $R$-modules which we call the little dimension. Using it, we extend the improved new intersection theorem.