in the case of a central simple algebra "a" over a field "f", the reduced norm provides a generalisation of the determinant giving a map "k"("a") → "f" and sk("a") may be defined as the kernel. wang's theorem states that if "a" has prime degree then sk("a") is trivial, and this may be extended to square-free degree. wang also showed that sk("a") is trivial for any central simple algebra over a number field, but platonov has given examples of algebras of degree prime squared for which sk("a") is non-trivial.