Abstract algebra/Quaternions

Introduction:

The set of all quaternions is denoted by H. The set of all quaternions is not a field because division is not defined on this set. So, H is a ring but not a field. Quaternions are like the complex numbers only with a few extras. These are: $i^2=j^2=k^2=-1$ and

$i*j=k,j*k=i,k*i=j$ positive cyclic permutation

$j*i=-k,k*j=-i,i*k=-j$ negative cyclic permutation.

Using quaternions it is possible to derive the Pauli Spin Matrices of Physics.