called , , , and . The notation is chosen such that plays the role of the additive identity element (denoted 0 in the axioms above), and is the multiplicative identity (denoted in the axioms above). The field axioms can be verified by using some more field theory, or by direct computation. For example,
: , which equals 1={{math}}, as required by the distributivity.

This field is called a finite field or Galois field with four elements, and is denoted or . The subset