Editing Skolem–Noether theorem (section)

== Statement ==
In a general formulation, let ''A'' and ''B'' be simple unitary rings, and let ''k'' be the center of ''B''. The center ''k'' is a [[field (mathematics)|field]] since given ''x'' nonzero in ''k'', the simplicity of ''B'' implies that the nonzero two-sided ideal {{nowrap|1=''BxB'' = (''x'')}} is the whole of ''B'', and hence that ''x'' is a [[Unit (ring theory)|unit]]. If the [[dimension (vector space)|dimension]] of ''B'' over ''k'' is finite, i.e. if ''B'' is a [[central simple algebra]] of finite dimension, and ''A'' is also a ''k''-algebra, then given ''k''-algebra homomorphisms

:''f'', ''g'' : ''A'' → ''B'',

there exists a unit ''b'' in ''B'' such that for all ''a'' in ''A''<ref>Lorenz (2008) p.173</ref><ref>{{cite book|last=Farb|first=Benson|title=Noncommutative Algebra|year=1993|publisher=Springer|isbn=9780387940571|author2=Dennis, R. Keith }}</ref>

:''g''(''a'') = ''b'' · ''f''(''a'') · ''b''<sup>−1</sup>.

In particular, every [[automorphism]] of a central simple ''k''-algebra is an [[inner automorphism]].<ref name=GS40>Gille & Szamuely (2006) p. 40</ref><ref name=Lor174>Lorenz (2008) p. 174</ref>