Would connecting propeller blades with a continuous ring reduce induced drag? Turbine engines are covered, which of course is to contain the process (just like a super/turbocharged engine is as soon as the air enters the intake). But it got me thinking, doesn't this also reduce - or even completely remove - the induced drag around the tips of the fan blades?

Would it be possible to have a similar setup for a standard prop, it doesn't even have to be stationary, it could be a ring connecting the tips of the prop, spinning with it, like an infinite winglet.  It has the added safety benefit that it'll be visible when the prop is spinning. And I figure if the ring is strong enough to maintain its circumference, the load on the prop should be marginal since it's spinning around its own center of mass.

Is the induced drag on the prop not large enough to warrant any thought, or would such a prop-winglet-ring (I'm sure there's a real name for it, anyone know what I'm talking about?) cause other disruptions of the airflow? Or perhaps there are other reasons, like it would simply be too hard to solve for constant-speed props?
What you're talking about does exist, they are called Q-Tip Propellers.

Remember that a propeller blade is just an airfoil - like a wing - and the basic aerodynamics are no different than a wing. But the rotation of the blade creates more phenomena than a wing, in particular the helicoidal vortex one sees behind the prop and causes all sorts of propeller effects.  

In theory, nothing would prevent us from having winglets at the prop tips :
the advantages would be


Making the prop more efficient by reducing the induced drag (same as a winglet on a wing )
Reducing noise
Keeping the propeller tip speed subsonic by decreasing its length


The big problem is in aerodynamic stresses, and as far as I know there have been some quite spectacular failures during testing, so the solution is now to give a greater sweep to the tips (see that as equivalent to the 777 wing tip compared to the 787 for instance). Try and find articles on the Hartzell Q-tip.

As naval propellers are wider and capable of deealing with bigger torque stresses, modern ones do have winglets. You could find some pictures on the web.