Kitchen sink?

Yes you can and here is more detailed info:

https://homeguides.sfgate.com/install-garbage-disposal-single-sink-52326.html

Hi Peggy, yes you can have a disposal on a single sink. A drop in sink sits on top of the counter top in a hole cut to size, an option that is the best when dealing with water. Under mount sinks are nice too, but you ill need the counter top to be finished in the cutout so it looks tidy so many under mount sinks are on stone counter tops and it is very important to put a bead of silicone all the way around the sink where it meets the counter top to prevent leaks that you don't notice right away

A drop-in sink has a visible lip around its perimeter that rests flat on the countertop. The sink basin drops straight into the countertop cut-out, and the perimeter lip holds everything in place. ... An undermount sink does have a rim, but the rim is not visible because it rests up against the bottom of the counter.

I guess it's all about what look you want, hope this link helps you out

https://faucetsreviewed.com/drop-in-vs-undermount-sinks/

A sink shouldn't be "a couple of buckets". The lift-over &/or reaching the bottom can be bad on your back and really, deep sinks aren't that useful except for hiding piles of dirty dishes. We installed a 2'x4' DARKROOM SINK to have an 8' square foot wet work area, and a vastly improved kitchen sink. We put a spray wand on the upper end and a regular faucet on the other, near the standard drain hole. A standard dispose-all can be installed. BTW to cut cost we used a plastic darkroom sink but will eventually replace it with stainless steel.

When my son had his house built, he went for one large sink. It is great! He likes to cook turkeys and he says it is perfect for cold water thaw. He has a disposal in his.

Yes you can put a disposal in single basin sinks