If the ring is unmarked, it’s safe to assume that the materials have no intrinsic value and the ring is decorative only.
Almost all gemstones used in mass market jewelry today are synthetic, and a small mounting such as this in, say, 12k would probably fetch you $15 at a jewelry store.
Best advice: if you like the ring, put it on and wear it! If your daughter or someone you like covets the ring intensely, it won’t be a mistake if you big ace it and give it to them.