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AsmAcTr. Let A be an n x m matrix (m > n) with entries in a noetherian ring R, let J be the ideal of R generated by the n x 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, ?2J 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].

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