Abstract
In this short note, we construct a right adjoint to the functor which associates to a ring equipped with a group action its twisted group ring. This right adjoint admits an interpretation as semilinearization, in that it sends an -module to the group of semilinear -module automorphisms of the module. As an immediate corollary, we provide a novel proof of the classical observation that modules over a twisted group ring are modules over the base ring together with a semilinear action.
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