We can use the existence of the splitting field to define reduced norm and reduced trace for a CSA "A". Map "A" to a matrix ring over a splitting field and define the reduced norm and trace to be the composite of this map with determinant and trace respectively. For example, in the quaternion algebra H, the splitting above shows that the element "t" + "x" i + "y" j + "z" k has reduced norm "t"2 + "x"2 + "y"2 + "z"2 and reduced trace 2"t".