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.

Related Topics:
Mathematics - Automorphism - Simple ring - Dimension - Field

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Then if

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:f,g : A → B

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

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:g(a) = b·f(a)b-1

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for all a in A.

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