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