Lens Nikon AF-S NIKKOR f/1.8G Lens - 50 mm Fits full frame bodies with out losing any resolution?

I know any DX lense can fit on a full frame body but they lose out and get dark rings around the images.

On amazon it says this is built for crop and full frame bodies… So on Dx body it would get 75mm and fX body it would give 50mm with out introducing outer dark ring?

The lens will have a 50mm focal length on any body. However, the field of view will be wider on a camera with a 135 sensor than on one with an APS-C sensor. On an APS-C sensor, it will have a similar field of view as a 75mm lens on a 135 sensor. The lens resolution will be the same on any body. The image resolution will depend on the sensor's resolution. As for vignetting and a 135 sensor, trust Nikon not to lie to you.

A 50mm lens will be 50mm on a full-frame body. It will also be 50mm on a crop-sensor body. Make no mistake. Lens focal length does not change!

What changes is angle of view. A 50mm lens on a crop-sensor body will "see" like a 75mm lens on a full-frame body. There's no need to concern with all these though. You simply shoot what you see.

That darker ring you are worried about happens only if you mount a crop-sensor (DX) lens to a full-frame body. DX lenses have smaller optical elements (glass pieces) and project a smaller image that will not fill up the entire full-frame digital sensor. The result is a small photograph with ugly large dark fuzzy borders. That is the least of your problems though. DX lenses have protruding rear elements and there's a chance it will get in the way of your full-frame camera's reflex mirror. A damaged mirror is a very expensive repair job!

Doing it the other way around poses no problem though so you can use FX lenses to your crop-sensor camera (as long as the mounts are the same). That's the reason why you can use the 50mm f/1.8G (an FX lens) with a crop-sensor body without problems.

Thanks for help