Hi Tuan,
Txs a lot for your quick reaction.
I have tested your solution and at first I had thought it wouldn't work... but actually this is because my configuration was a bit more complex than what I summarized in my question.
But your answer put me on the right way.
In fact, I had created 1 edocman category named "public" (with many subcategories) and 1 edocman category named "private" (with many subcategories).
So actually it was not in the general "options" you mentionned I had to make my changes, but in the "permissions" of my "private" category.
So there I set the access of "public" to "inherited" on the line "download".
For the registered users, I have in fact 4 levels ("associate", "regular", "mandat." and "board").
Sor for each of these 4 levels I set the access to "allowed" on the line "download".
And so far in my testings it seems to work.
So txs again Tuan for showing me the way.
PS : here is the screenshot of the configuration of my edocman category "private"