On Hasse--Schmidt derivations: the action of substitution maps

TL;DR

This paper explores how substitution maps act on Hasse--Schmidt derivations, revealing an algebraic structure analogous to classical derivations' module structure.

Contribution

It introduces a new algebraic framework for understanding the action of substitution maps on Hasse--Schmidt derivations, expanding their structural theory.

Findings

Substitution maps induce a novel algebraic structure on Hasse--Schmidt derivations.

The structure parallels the module structure of classical derivations.

This framework enhances the understanding of derivations in power series rings.

Abstract

We study the action of substitution maps between power series rings as an additional algebraic structure on the groups of Hasse--Schmidt derivations. This structure appears as a counterpart of the module structure on classical derivations.