Nuclear modules over a topological ring

Question

Let $A$ be an $\mathbb R$ or $\mathbb C$ algebra. (You may assume $A$ is nuclear and Frechet)

1. Is there a notion of Nuclear modules over $A$, which extends the notion of a nuclear TVS over $\mathbb R$ or $\mathbb C$? In particular, I am looking for a definition of nuclear modules, for which if $B$ is a nuclear TVS (over $\mathbb R$ or $\mathbb C$), then $A\widehat\otimes B$ is a nuclear module over $A$.
2. If such a definition exists, is it clear that $\hom_A(C,A)$ is nuclear over $A$, whenever $C$ is nuclear over $A$?
3. What would be the analogues of barreled, Frechet and montel spaces over $A$?

I could guess one such definition would be that a module $C$ over $A$ is nuclear if the $\epsilon$ and the $\pi$ topologies on $C\widehat \otimes_A D$ are the same, for all $A$-modules $D$. However, I do not know how to define or prove any qualities of such spaces...

I found this article, but my mathematics is not strong enough to make sense of it. (https://arxiv.org/pdf/2002.11608.pdf)