Skolem-Noether theorem

In mathematics, the Skolem-Noether theorem is a result on automorphisms of simple rings. In a general formulation, let A and B be simple rings, and K = Z(A) be the centre of A. Suppose that the dimension of A over the field K is finite.

Then if

f,g : A → B

are K-algebra homomorphisms, there exists a unit b in B such that

g(a) = b·f(a)b^-1

for all a in A.