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Extra resources for Emmy Noether in Bryn Mawr: Proceedings of a Symposium Sponsored by the Association for Women in Mathematics in Honor of Emmy Noether’s 100th Birthday

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52 (1965). I 19. J-L. I-J. Sansue. La R-equivalence sur les tores. Ann. Sci. , 101 (1977). 175-2~O. [CTS] [DMil F. De Meyer and E. Ingraham. Separable Algebras ot'eT Commutative Rings. Lecture Notes in Math .. IXI Springer-Verlag: Berlin, Heidelberg, New York, 1971. [EMI] S. Endo and T Miyata. Invariants of finite abelian groups. J. Math. Soc. Japan, 25 (1973), 7-26. S. Endo and T. Miyata. Quasi-permutation modules over finite groups, I, II. J. Math. Soc. 397-421 and 26 (1974), 689-713. [EM2] [EM3] S.

Hochster. Topics in the Homological Theory of Modules over Commutative Rings, CBMS Conf. Ser. , 24 (1974). [H-E] M. Hochstcr and 1. A. Eagon. Cohen-Macaulay rings. invariant theory. and the generic perfection of determinantalloci. Amer. l. • 93 (1971). 1020-1058, [K] W. Krull. Zum Dimensionsbegriff der Idealtheorie. Math, Z,. 42 (1937), 745-766. [L] S. Lang, Introduction to Algebraic Geometry. New York: Interscience, 1958. [P-S] C. Peskins and L. Szpiro, Dimension Projectil'e Finie et Cohomologie Locale.

Let ME 2". Then (a) ME ff'" <=> H-1(n', M) = 0 for alln' c n. (b) ME C(J" <=> H1(n', M) = 0 jar alln' c n. 2(b) it will suffice to prove (b). 1(a). 4. 9,. c ~" n C(J". Proof Since ~" and C(J" are closed under direct sums and direct summands it is enough to check that modules of the form P = Zn/n' lie in them. (Z) and H1(n', Z) = Hom(n', Z) = O. For ~"we use the involution M 1--+ M to reduce to the case just done. 5. If M E 2", there are exact sequences: (a) 0 -+ M -+ P -+ F -+ 0 with FE~" and PE Perm".

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