Rings don't display when placed on the subscreen in ZQuest. They do, however, show up in the player
(Tested in Windows build 288)
Rings On The Subscreen
When previewing equipment, ZQ used to only show the level 1 version of that item if it exists, and nothing otherwise. Since for some reason the blue ring starts at level 2, nothing was therefore displayed.
Starting with the next build, ZQ will try to display the item of lowest level of the particular class, instead of just the level 1 item. The only exception is the shield; ZQ is still hard-coded to try to display the shield of level 2 (typically the magic shield).