Ringworm is not a parasite, its a fungal skin infection. So yes it can appear on a dogs stomach, but its more likely to be a sting or bite of some sort, even a nettle rash. Try using an antiseptic cream (even diaper cream) for a couple of days and if it doesn't help get it checked by a vet
Yes it is a fungus, but you need to treat it with an antifungal cream like lamisil. you should treat it twice a day for 3 weeks or more, be careful for it can spread to you also! go to wal-mart and buy some jock itch cream and use that. thats what we recommend in our clinic.
Ring worm is a parasite, so I'm pretty sure it could get on a dog as easily as it does a human.