addition is a usual operation, except multiples of p should be left out of the set (modulo p). This type of field should not be confused with finite fields because also has multiplication as an operation. Vectors over are denoted , where is the number of elements in the vector. The sum of any two vectors in would be mod p.

has 4 elements in each vector

has 6 elements

The additive identity is true for , so . For every element there is another element where .

3mod(5) + (-3)mod(5) 3 + 2 0

1mod(5) + (-3)mod(5) 1 + 4 0

2mod(5) + (-3)mod(5) 2 + 2 0