By Hiroaki Hijikata

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**Extra info for Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 1**

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Sem. Mat. Univ. Torino, 42(1984), 65-88. [2] S. S. Abhyankar : Enumerative Combinatorics of Young Tableaux, Marcel Dekker, New York, forthcoming. [3] P. Doubilet - G. C. Rota - J. Stein : Foundations of combinatrics IX: Foun dations of combinatorial methods in invariant theory. Stud. Appl. , 53(1974), 185-216. [4] E. Pascal : Mem. del R. Acc. dei Lincei, Series V, 4a(1888). [5] A. Young : On quantitative substitutional analysis I, Proc. London Math. Soc, 33(1901) 97-146. Shreeram S. A. Poona University Pune 411007 India Bhaskaracharya Pratishthana Pune 411004 India Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Ν AG ATA pp.

Dubreil 1977/78, Lect. Notes in Math. 740, Springer Verlag, 1979, 213-229. G. Valla, Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537-548. Yoichi AOYAMA Department of Mathematics Faculty of Science Ehime University Matsuyama, 790 Japan Shiro G O T O Department of Mathematics College of Humanities and Sciences Nihon University Setagaya-ku, Tokyo, 156 Japan Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Ν AG ATA pp. 35-44 (1987) A Structure Theorem for Power Series Rings Michael ARTIN and Christel ROTTHAUS The object of this paper is to prove the following result, which was announced in [3] for the case that Ä is a field of characteristic zero.

N Let R = R{A,J), ... = mi? -f generated A-algebra). = Note that R has a duaUzing complex (as Ä is a finitely T h e o r e m 3 . 1 . , 0^, (cf. 17] and [15,§1]). We put p = φη A. First suppose p is not a maximal ideal. If p 2 then Rp = Ap[T] is CohenMacaulay. 19]. Hence Rφ is Cohen-Macaulay. Now suppose p is a maximal ideal. Considermg Ap and Rp instead of A and R respectively, we may assume that A is a local ring. , yx^^)r-' and φ 2 Φ ^ x^T or φ ^ yx^T for some i. Without loss of generality we may assume φ ^ xl^'T or φ ^ yxlT, Suppose φ ^ xl'^T.