Are they nicotine stains or burns in the surface? You should just be able to remove stains with soap and water or a mild abrasive cleaner. You can't remove burns but you could try sanding them with very fine grit sand paper to remove the burn and any raised melted edges then colouring them in with marker pen or paint the same colour as the floor to disguise them. You could also ask advice at a linoleum supply shop.
I'd try ammonia straight from the bottle and see if that worked.
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Nicotine can leave ugly brown stains on many surfaces. There are several products you can try and you may need to do some scrubbing with a brush to remover particularly stubborn stains. This is a page about how to remove nicotine stains on a vinyl floor.