Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Not sure it helps but (if I'm not mistaken) the condition is clearly equivalent to $\text{Hom}_R(A,B)=\text{Hom}_{\mathbb Z}(A,B)$ for all $R$-modules $A$ and $B$.
Thanks a lot!!! Sadly I don't know enough algebraic geometry to fully understand your answer. But I'll still ask you an elementary question. It seems to me you could set $r_n:=n$ throughout, because when you prove the lemma, you start with arbitrary $n$ and $r$. Am I right?
@EhudMeir - Thanks! You posted your second comment while I was writing the following answer to your first comment. In the definition of $A=K[[x_1,x_2,\dots]]$ that I gave (and which I found in Bourbaki), the notation $\sum_ua_uu$ is completely formal. In other words, this formal sum represents an element of $A$, but not the sum of a series. To say it in yet another way, $A$ is not defined as the $(x_1,x_2,\dots)$-adic completion of $K[x_1,x_2,\dots]$.
I hope the title and the posts will be edited, but the current title and the current post mention "Masaki Kashiwara's book Sheaves on Manifolds", although the book has two authors, Masaki Kashiwara and Pierre Schapira.
@ĐàoThanhOai - The usual terminology is to call elements of $\mathbb Z$ integers, and to say that an integer $n\in\mathbb Z$ is nonnegative if $n\ge0$ and positive if $n>0$. Also, if you want a user to be notified, you can use the @ symbol.
