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The Cohen-Macaulayness of the Rees algebras of local rings

Published online by Cambridge University Press:  22 January 2016

Shin Ikeda
Shin Ikeda*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusaku, Nagoya, 464, Japan
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Let (A, m, k) be a Noetherian local ring. We define

and call it the Rees algebra of A. Let X be an indeterminate over A, then R(A) can be identified with the A-subalgebra .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 89 , March 1983 , pp. 47 - 63
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[ 1 ] Auslander, M. and Buchsbaum, D. A., Codimension and multiplicity, Ann. of Math., 68 (1958), 625–657.CrossRefGoogle Scholar
[ 2 ] Goto, S. and Shimoda, Y., On the Rees algebras of Cohen-Macaulay local rings, Commutative algebra (analytic methods), Lect. Notes in Pure and Appl. Math., 68 (1982), 201–231.Google Scholar
[ 3 ] Goto, S. and Shimoda, Y., On Rees algebras over Buchsbaum rings, J. Math. Kyoto Univ., 20 (1980), 691–708.Google Scholar
[ 4 ] Grothendieck, A., Local cohomology, Lect. Notes in Math., 41, Springer Verlag, Heidelberg, 1967, 116 pp.Google Scholar
[ 5 ] Matijevic, J. and Roberts, P., A conjecture of Nagata on graded Cohen-Macaulay rings, J. Math. Kyoto Univ., 14 (1974), 125–128.Google Scholar
[ 6 ] Northcott, D. G. and Rees, D., Reductions of ideals in local rings, Proc. Camb. Phil. Soc, 50 (1954), 145–158.Google Scholar
[ 7 ] Renschuch, B., Stuckrad, J. and Vogel, W., Weitere Bemerkungen zu einem Problem der Schnittheorie und uber ein Maß von A. Seidenberg fur die Imperfektheit, J. Algebra, 37 (1975), 447–471.Google Scholar
[ 8 ] Schenzel, P., Applications of dualizing complexes to Buchsbaum rings, Adv. in Math., 44 (1980), 61–77.Google Scholar
[ 9 ] Schenzel, P., Trun, N. V. gand Cuong, N. T., Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr., 85 (1978), 57–73.Google Scholar
[10] Stuckrad, J. and Vogel, W., Eine Verallgemeinerung der Cohen-Macaulay Ringe und Anwendungen auf ein Problem der Multiplzitatstheorie, J. Math. Kyoto Univ., 13 (1973), 513–528.Google Scholar
[11] Stuckrad, J. and Vogel, W., Toward a theory of Buchsbaum singularities, Amer. J. Math., 100 (1978), 727–746.CrossRefGoogle Scholar
[12] Valla, G., Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537–548.Google Scholar