Leaps of modules of integrable derivations in the sense of Hasse-Schmidt

TL;DR

This paper proves that in characteristic p > 0, the jumps in the chain of modules of integrable derivations (Hasse-Schmidt) only occur at powers of p, revealing a specific pattern in their structure.

Contribution

It establishes that leaps in modules of integrable derivations happen exclusively at powers of p, clarifying their behavior in characteristic p > 0.

Findings

Leaps occur only at powers of p.

Modules of integrable derivations follow a predictable pattern.

Provides insight into the structure of derivations in characteristic p.

Abstract

Let k be a commutative ring of characteristic p > 0. We prove that leaps of chain formed by modules of integrable derivations in the sense of Hasse-Schmidt of a k-algebra only occur at powers of p.