I assumed that all rings are a part of a ritual magic and share the same spell.
Your ring is bound to you as part of a ritual when it is made for you and inscribed with 3 words of OBS. One of the things about the rings is that they only work for you. The core of the ritual probably needs redoing every year, but that maintains the rings.
When you are wearing your ring you can see the inscription of the 3 letters of other rings through the body of the ring, if you can physically see their ring.
As for checking out the ring someone is wearing. Think of it as cruising a bar making sure that person you are trying to pick up doesn't have a wedding ring on. It might be noticed that you check out rings on people when you meet them, but probably not. I leave it up to the DM to decide what DC's are appropriate and what excuses are used if noticed.
Your ring is bound to you as part of a ritual when it is made for you and inscribed with 3 words of OBS. One of the things about the rings is that they only work for you. The core of the ritual probably needs redoing every year, but that maintains the rings.
When you are wearing your ring you can see the inscription of the 3 letters of other rings through the body of the ring, if you can physically see their ring.
As for checking out the ring someone is wearing. Think of it as cruising a bar making sure that person you are trying to pick up doesn't have a wedding ring on. It might be noticed that you check out rings on people when you meet them, but probably not. I leave it up to the DM to decide what DC's are appropriate and what excuses are used if noticed.