They look good. A few suggestions. The white balance looks off, or you're not using a white backdrop. This was distracting to me because everything looks yellow. You can also see reflections of either you or something else in the ring in the last and second to last photo.

Also with reflective object, the flash will reflect off the object as it is. So a square softbox will make a square reflection (bright spot), a umbrella will make a round bright spot, a beautydish or reflector will do the same. I'm not sure what types of light modifiers you have at your disposal, but this is one thing to keep in mind while doing highly reflective product photography.

Since you're only using one flash, I would suggest using a couple white pieces of foam board or paper, and bouncing the flash off them to get rid of those shadows on the first two photos.

Your composition is nice and the white balance is an easy fix in PS. Your wife must be very happy for such a nice gift!