Skolem-Noether theorem
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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.