Say we have the set of real numbers. Can we construct a different ring than the usual ring of real numbers?
I am trying to wrap my head around the idea of rings and I couldn't find two other operations that will hold distributive property other than usual addition and multiplication.
If we can find another ring with the set of real numbers, is there a set with only one ring structure? If we can't find another ring with the set of real numbers, is there a set with different ring structures?