Completely m-full ideals and componentwise linear ideals

TL;DR

This paper proves that in a polynomial ring over an infinite field, the class of completely m-full ideals is exactly the same as the class of componentwise linear ideals, establishing a key equivalence.

Contribution

It establishes the equivalence between completely m-full ideals and componentwise linear ideals in polynomial rings over infinite fields.

Findings

Complete characterization of the equivalence between the two classes.

Simplification of understanding the structure of these ideals.

Potential implications for ideal theory and algebraic geometry.

Abstract

We show that the class of completely m-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field.