Kind of got it to work : i know have the id displayed in my div.
That's already a big step ahead, thanks.
Know i must figure out another thing : how to do a query to get the "machine_name" and not its id...
Just to let you know, i had to change the view.html.php file associated with the view of the "machines" table, where there is a
$event = 'jQuery("#jform_machine").val(this.value);';
That i modified with
$event =
'
jQuery("#jform_machine").val(this.value);
var machine = "";
machine = jQuery("#jform_machine").val();
jQuery("#machine").html(machine);
';
with #machine being the div displaying the actual result in the view