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On a criterion of exactness of a finite free complex

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Abstract

In this paper we prove the sufficiency of a criterion of exactness of a complex of finitely generated free modules over a commutative ring, which was known earlier for the case of a complex over a Noetherian ring.

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Literature cited

  1. D. A. Buchsbaum and D. Eisenbud, “What makes a complex exact?” J. Algebra,25, No. 1, 90–99 (1973).

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  2. J. A. Eagon and D. G. Northcott, “On the Buchsbaum-Eisenbud theory of finite free resolutions,” J. Raine Angew. Math.,262–263, 205–219 (1973).

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  3. A. Barger, “A theory of grade for commutative rings,” Proc. Amer. Math. Soc.36, No. 2, 365–368 (1972).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. V. Shekhtman

Authors
  1. V. V. Shekhtman
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Additional information

Translated from Matematicheskie Zametki, Vol. 17, No. 5, pp. 711–716, May, 1975.

The author is thankful to E. S. Golod for taking interest in this paper.

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Shekhtman, V.V. On a criterion of exactness of a finite free complex. Mathematical Notes of the Academy of Sciences of the USSR 17, 422–425 (1975). https://doi.org/10.1007/BF01155796

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  • DOI: https://doi.org/10.1007/BF01155796

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