n-trivial extensions and multi Hasse-Schmidt derivations

TL;DR

The paper introduces a generalized concept of Hasse-Schmidt derivations that aligns with n-trivial extensions, supported by numerous examples and foundational properties.

Contribution

It presents a new generalization of Hasse-Schmidt derivations corresponding to n-trivial extensions, expanding the theoretical framework.

Findings

Established the equivalence between the generalized derivations and n-trivial extensions.

Provided multiple examples illustrating the new generalization.

Proved fundamental properties of the generalized derivations.

Abstract

We propose a generalization of Hasse-Schmidt derivations that is equivalent to the notion of n-trivial extension introduced by Anderson-Bennis-Fahid-Shaiea, in the same way that derivations are equivalent to trivial extensions. We provide many examples of this generalization and prove some of its basic properties.