A field, K, has 2 binary operations (+,*) The field is an abelian group under "+" for multiplication

1. There exists a unique inverse, a^ forall a in K - {0} ({0} is the

   zero for "+")

2. a(bc)=(ab)c (associativity)
3. a(b+c)=ab+ac (distributivity)
4. There exists an identity e, s.t. ae=ea=a

Examples

1. R
2. C
3. H = Quaternions