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On the grade of some ideals

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Abstract

An “additivity” formula is obtained for the grade of an ideal in a residue ring R/I, where I is a perfect ideal. This result is then applied to compute the grade of ideals of linear (inhomogeneous) polynomials. Further results on the homological rigidity of the conormal module I/I2 are pointed out. Finally, an elementary proof is given of a result of Buchsbaum concerning the grade of ideals of minors of a matrix.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal da Bahia, Rua Caetano Moura 99, Federação, 40.000, Salvador, BA, Brasil

    J. F. Andrade

  2. Instituto de Matemática Pura e Aplicada (IMPA), Rua Luis de Camões 68, Centro, 20.060, Rio de Janeiro, RJ, Brasil

    A. Simis

  3. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    W. Vasconcelos

Authors
  1. J. F. Andrade
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  2. A. Simis
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  3. W. Vasconcelos
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Partially supported a CNPq grant

Partially supported by NSF and CNPq grants

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Andrade, J.F., Simis, A. & Vasconcelos, W. On the grade of some ideals. Manuscripta Math 34, 241–254 (1981). https://doi.org/10.1007/BF01165538

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