A non empty set R that has two binary operations, addition and multiplication, satisfying:

1. a + b = b + a, for a,b∈R.

2. (a + b) + c = a + (b + c) for a,b,c∈R.

3. There is an element 0 in R such that a + 0 = a for all a∈R.

4. For every element a∈R, there exists an element −a in R such that a+(−a)=0.

5. (ab)c=a(bc) for a,b,c∈R.

6. For a,b,c∈R,

a(b + c) = ab + ac

(a + b)c = ac + bc. ;