Identify a spell effect that is in place is a DC 20+spell level knowledge (arcana) check. Without that, knowing that the circle of toadstools isn't a prank or odd random magic effect in the dungeon-like area depends on how well an observer knows the area, and I suppose on how likely that is in this particular area.
Detect magic or similar could gather more info once the ring is noticed if the observer doesn't have knowledge (arcana).
Of course, if the toadstools are in a dark room which no one enters and so no one actually sees the ring, all of the above is irrelevant and the PCs are safe.
what you should be asking is what happen if the one finding the toadstools go "oh wow! so many tasty mushrooms, lucky me!" and go around picking them...
it would first depend on the location. If it's in an area where mushrooms might naturally occur like a forest or musty dungeon, then they would probably be ignored. If they were in a pristine castle with polished marble floors, then they might be noticed. Once noticed it would then take a detect magic to determine of they were magic, and the knowledge(Arcana) check to determine what spell they were associated with.
So IMO 3 potential checks
1. Perception to see
2. Detect magic determine if magical (this isn't really necessary)
3. Knowledge Arcana to determine spell
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Good answers on the mechanics above.
If you're looking for advice: if it's in a dank corner of a dungeon or natural cave, I'd just congratulate them on their cleverness and move on. If they put it in the middle of a well-traveled, well-lit corridor then I'd probably have some guards stationed around it when they come out (if someone in the dungeon has magical skills and can recognize the spell) or some really shocked cleaning staff it they don't. The PCs will be rested so it's not like you're being unfair to them. Environment in-between? Whichever seems like more fun.