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Let 7<" be a field, G a group of automorphisms of K, and M a vector space over K on which G acts in such a way that a(aD) = aa-crD for &EG, aEK, and DEM. The problem arises to find whether M has a basis consisting of invariant elements under G. In other words, letting K0 be the fixed field under G, and M0 the set of fixed elements of M under G so that Mo is a vector space over Ko, to find out whether M is isomorphic to the tensor product M « K ®K, Mo under the natural map. We shall see thatdoi:10.2307/2032732 fatcat:6mza6qbnqneg3h6asbd5juzikm