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On the height of ideals generated by matrices


Author: Joseph Becker
Journal: Proc. Amer. Math. Soc. 51 (1975), 393-394
MSC: Primary 32B15; Secondary 13C15
DOI: https://doi.org/10.1090/S0002-9939-1975-0385150-6
MathSciNet review: 0385150
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Abstract: A short geometric proof of the following algebraic theorem of Buchsbaum and Rim: Let $ R$ be the reduced local ring of an analytic variety and $ g:{R^t} \to {R^r},t \geq r$, be a homomorphism of $ R$ modules. Then the codimension of the support of the cokernel of $ g \leq t - r + 1$.


References [Enhancements On Off] (What's this?)

  • [1] D. A. Buchsbaum, A generalized Koszul complex. I, Trans. Amer. Math. Soc. 110 (1964), 183-196. MR 28 #3075. MR 0159859 (28:3075)
  • [2] D. A. Buchsbaum and D. S. Rim, A generalized Koszul complex. II: Depth and multiplicity, Trans. Amer. Math. Soc. 111 (1964), 197-224. MR 28 #3076. MR 0159860 (28:3076)
  • [3] J. Lipman, Free derivation modules on algebraic varieties, Amer. J. Math. 87 (1965), 874-898. MR 32 #4130. MR 0186672 (32:4130)
  • [4] D. Mumford, Introduction to algebraic geometry, Harvard Univ. Press, Cambridge, Mass.
  • [5] R. Narasimhan, Introduction to the theory of analytic spaces, Lecture Notes in Math., no. 25, Springer-Verlag, Berlin and New York, 1966. MR 36 #428. MR 0217337 (36:428)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0385150-6
Keywords: Height of ideal generated by matrices
Article copyright: © Copyright 1975 American Mathematical Society

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