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Ideals of analytic deviation one with respect to a Cohen-Macaulay module

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  • Ganesh S. Kadu

    (IIT Bombay)

Abstract

Let (A, m) be a Cohen-Macaulay local ring, M a Cohen-Macaulay A-module of dimension d ≥ 1 and I a proper ideal of analytic deviation one with respect to M. In this paper we study the Cohen-Macaulayness of associated graded module of a Cohen-Macaulay module. We show that if I is generically a complete intersection of analytic deviation one and reduction number at most one with respect to M then G I (M) is Cohen-Macaulay. When analytic spread of I with respect to M equals d we prove a similar result when reduction number of an ideal is atmost two.

Suggested Citation

  • Ganesh S. Kadu, 2011. "Ideals of analytic deviation one with respect to a Cohen-Macaulay module," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(2), pages 73-97, April.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:2:d:10.1007_s13226-011-0005-9
    DOI: 10.1007/s13226-011-0005-9
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