Let $ X $ be an affine, normal, $ \mathbb{G}\_{a} $-variety with action $ \beta $ over a field $ k $ of characteristic zero. The action of $ \mathbb{G}\_{a} $ is obtained from $ \delta \in \operatorname{Der}\_{k}(\mathcal{O}(X)) $ via
\begin{align\*}
\beta^{\sharp}(f) =\exp(t\delta)(f)\\
= \sum\_{j=0}^{\infty} \frac{\delta^{j}(f)t^{j}}{j!}.
\end{align\*}
The plinth ideal is the ideal of $ \mathcal{O}(X)^{\mathbb{G}\_{a}} $ generated by all elements $ h $ such that there exists a $ g \in \mathcal{O}(X) $ such that $ \delta(g)=h $. The first paper I could find with this name usage was one by Dufresne and Kraft ([Invariants and Separating Morphisms for Algebraic Group Actions](https://doi.org/10.1007/s00209-015-1420-0)). Does anyone have any earlier references with this name usage or concept?



Does anyone know the first times the term plinth ideal of a $ \mathbb{G}_{a} $-representation was used?
G. Freudenburg, in [Algebraic theory of locally nilpotent derivations](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.470.10&rep=rep1&type=pdf) introduces the term "plinth ideal" in a way that suggests it was not used before, on page 10, with the footnote:


*The term plinth commonly refers to the base of a column or statue.*


S. Kuroda, in [arXiv:1412.1598](https://arxiv.org/pdf/1412.1598.pdf) writes that *"the notion of plinth ideal already appeared in Nakai (1978), although not called by this name."*


