# Polynomial invariants of finite groups by D. J. Benson By D. J. Benson

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Is Assume that a C is locally projective, bA is flat and A /B is C-Galois. e. cr[A*c] = (^[C*c]i injective, for every M G ; an isomorphism, for every A-generated M G . Proof 1. Since A /B is C-Galois, is an isomorphism, hence C is Agenerated. Consequently cr[A*c] ^ £ ^[-^*c]j he. cf[A*c] = cr[C*c]2 . 22] applies. 3. U M £ MP is A-generated, then is surjective, hence bijective by ( 2). 13] (which is itself a generalization of [14, Theorem 2 . 11]). 2. Assume that A /B is C-Galois. 1. If b A is flat, then satisfies the weak structure theorem.

A, A ^ A(M) and Ti. + {n~'^)u + Dv + Duv \{M ) = A(M). 5. i-order. If F is a maximal D-order then it is also an W-order and thus a maximal W-order. Proof. Since L is an 7i-lattice, A(L) is an W-order and since L is a left ideal for F, we have F C A(L). The other statement is obvious from this. 3, we may obtain a first char­ acterization of maximal W-orders in terms of maximal orders. If A is a maximal H-order in A, then there is a maximal order F in A such that A = \{ H —^ F) = p{H —^ F). 6. Proof.

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