b * sqrt(0)? But yeah, the integers form a ring in their own right. They call the new system a ring, but that doesn't mean the old system wasn't also a ring.

b * sqrt(0)? But yeah, the integers form a ring in their own right. They call the new system a ring, but that doesn't mean the old system wasn't also a ring. Also not all rings are of that form - as you say a ring is a very general algebraic structure.