Can a bezel be riveted instead of soldered?
If you're talking about wire bezels for setting, then you can't
rivet them closed; they won't hold a stone effectively if there is a
split in the bezel. You can, of course, rivet them to the support
structure, whatever that may be.
If you want to close a bezel with rivets you should use thicker
sheet to make the bezel so that the interrupted section will get its
strength from the thickness of the metal rather than from the tension
of the deformed circumference.
Think about a dog tooth setting. If it's made in really thin sheet
the teeth will easily open, but in thicker sheet they'll keep the
stone in place.
Yes, a bezel cup can be riveted, but use two rivets to prevent
rotation, unless rotation doesn't matter. Just set the stonein the
usual manner after the bezel cup is in place. A spacer may be
required to allow the back of th stone to clear the rivet heads if
the latter are not countersunk.