I've been through something similar to this and it's not a pleasant feeling. You've got my sympathy.
I see that you feel the relationship is serious but when she still wears that ring, she's clearly sending out the wrong message - giving you feelings that she's ambivalent - a recipe for potential heatache for you.
Perhaps you could have a heart-to-heart chat with her and explain in non-accusatory or non-judgemental terms that you want to this relationship to progress and prosper but with her wearing that ring and keeping c0nstant reminders ever-present, it's putting you off and cramping your style.
Of course, she has to know that you're not trying to replace him, but your relationship needs some space to grow without those constant reminders in your faces. Perhaps she can have a room in her home with some keepsakes, but memories all over the place is a turn-off for you.
This could be that it's just an awareness issue, but maybe not. Has she gone through any counseling or therapy? There are probably some great grief-therapy groups she could attend (or did?)
Regardless of all that, many widows remove clothes from their clothes closet fairly quickly..like within a month or two. She perhaps hasn't made the kind of progress with her grief as would warrant for a intimate relationship. We all grieve at different rates, but to me it sounds as though it's not working out for you, at least. Maybe, it something that could change with time...or maybe this isn't her time for an intimate relationship right now
Here's my personal experience
My fairly recently experience with this dating of a widow was somewhat parallel and reasonably similar. I dated a widow (hubby passed 3 yrs prior) for 11 months. She'd gone though some long term grief therapy (his was a suicide) and was still in a grief counseling group.
After seeing her for more than 3 months, I had that heart-to-heart discussion about presence of photos, etc. She removed the hanging ones from her bedroom. This helped a lot as we were an intimate couple. However, she had some still in the living room/TV room of her and her late hubby, which did not come down. I wasn't happy about that but it wasn't a show-stopper.
Ultimately, there was no way for us to progress as her loss was part of her every-day life in a way that just didn't work. My goal was not to just have someone to see date-wise, but to have a partner. After almost one year this wasn't the sort of relationship I felt that I could settle down with. Maybe your goals and situation is different, though.
The bottom line is have a heart-to-heart with her and tell her your concerns about the relationship's future and see where she is at with this. She may surprise you and maybe she just needs to know how those reminders affect you. Maybe it is something she can modify or change! People do grow and soemtimes need a gentle push.