There are other classifications of mathematical systems
Chapter 10, Problem 10.1.42(choose chapter or problem)
There are other classifications of mathematical systems besides groups. For example, there are rings and fields. Do research to determine the requirements that must be met for a mathematical system to be (a) a ring and (b) a field. (c) Is the set of real numbers, under the operations of addition and multiplication, a field? Ask your instructor for references to use.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer