In my dinning room I have two 3-way switches that control the light. I
replaced one of the 3-way switches with a 3-way dimmer (GE push on/off).
After connecting everything, the dimmer acts as a "master" switch. If the
dimmer switch is on, the other 3-way switch can turn the light on or off. If
the dimmer switch is off, the other 3-way switch has no affect and the light
stays off.

Is this how it is supposed to work? Or did I wire something incorrectly?

The dimmer has four wires grouped in two's. A black/red pair and a
black/green pair. I identified the hot wire in the box and connected it to
the black wire of the black/red pair. I then connected the red and other
black wire to the remaining two wires in the box without identifying them.
The green wire was then connected to the ground.

Any help would be greatly appreciated,

Rich