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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A complex that resolves the ideal of minors having $ n-1$ columns in common


Authors: J. F. Andrade and A. Simis
Journal: Proc. Amer. Math. Soc. 81 (1981), 217-219
MSC: Primary 13D25; Secondary 14M12
MathSciNet review: 593460
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Abstract: Let $ A$ be an $ n \times m$ matrix $ (m \geqslant n)$ with entries in a noetherian ring $ R$, let $ J$ be the ideal of $ R$ generated by the $ n \times n$ minors that are formed with $ n - 1$ fixed columns of $ A$. Necessary and sufficient conditions are given in order that a suitably defined complex be a free resolution of the $ R$-module $ R/J$. The complex is closely related to the complexes of Buchsbaum-Rim [2, §2] and it is perhaps worthwhile mentioning that a special case of the present result was obtained by Buchsbaum-Eisenbud in a different context [1, Theorem 8.1].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0593460-5
PII: S 0002-9939(1981)0593460-5
Article copyright: © Copyright 1981 American Mathematical Society