Rings of constants of linear derivations on Fermat rings

TL;DR

This paper characterizes all linear complex derivations of Fermat rings, revealing their structure and providing explicit examples, thereby advancing understanding of derivations in algebraic geometry.

Contribution

It provides a complete characterization of linear derivations on Fermat rings and constructs explicit examples, a novel contribution to algebraic derivation theory.

Findings

Fermat rings have linear complex derivations with trivial constants.

Complete classification of linear derivations on Fermat rings.

Explicit examples of such derivations are constructed.

Abstract

In this paper we characterize all the linear $\mathbb{C}$-derivations of the Fermat ring. We show that the Fermat ring has linear $\mathbb{C}$-derivations with trivial ring of constants and construct some examples.