Product review (3 stars): Pretty good, but there was a little problem (fixable).
Upon going to the Sears Kenmore website I found that the part number of this thing is a substitute for WD26X10013, the one that I really needed. And I found that indeed it surely seems to be that--- it very closely resembles the old assembly that I removed.

I should add that it's wonderfully complete with regard to adaptor cables, hoses and even mechanical supports and bolts, etc. And so I had no problem with installation.

However, I soon found that there was a problem with the drain cycles not ending as the fill cycle began, causing not enough water to be accumulated in the basin. Upon investigation, the valve that switches back and forth between drain and spray was sticking, not going back to the spray setting after the solenoid that controls the draining was switched off.

My surmise was that if the spring on the solenoid were to be strengthened--- I'm talking about the vertical one that connects to the rocker arm on the pump valve stem--- then that might cure the problem. So I got the spring off of the old unit and thereby doubled up the spring tension on the new one.

My guess is that if I had gone to 1 1/2 times the tension instead of 2 times, that would have been better as now the draining may be being curtailed a bit too soon. But I think that this is a stable way to operate it, and so I'm happy with it. And the dishes are clean.

In all, it's a substantial piece of equipment for a reasonable price. I'm left with a minor leak around the boot, not the fault of this device. With my experiences, had I looked at prices for new dishwashers which are lower than I had thought, I might have gone that route.