The ring of quaternions, discovered by W.R. Hamilton provides the most often cited example of a skew field or division ring it consists of all possible sums of the form

* a1 + bi + cj +dk*

where * a,b,c * and * d* are real numbers and
* 1,i,j * and * k* are members of the quaternionic group.
For concreteness we can take * 1,i,j * and * k* to
be * 4 x 4 * matrices:

1 = 1 0 0 0 i = 0 -1 0 0 j = 0 0 -1 0 k = 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 1 0 0 0

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

An On-line Dictionary of Combinatorics