Example

Let f = X² + X + 1 be a polynomial in R = Z/2Z[X]. Then f is irreducible. The field K = R/(f) has 4 elements:

0, 1, a = X + (f), a + 1.

The multiplication table of the set K* of invertible elements (in the case of a field this coincides with the set of nonzero elements) is as follows:

·	1	a	a + 1
1	1	a	a + 1
a	a	a + 1	1
a + 1	a + 1	1	a