Abstract
Let R be a commutative noetherian ring with identity. To a finite free resolution F of an R-module M and every integer p⩾1 we associate finite free complexes C p* F. C p* F is a free resolution of P∧M-the p-th exterior power of M if the degree of torsionfreeness of M is large enough. Using C p* F we further study the degree of torsionfreeness of P∧M. As an application we prove a special case of a conjecture of P. Hackman concerning a connection between rank and torsionfreeness of a module.
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Lebelt, K. Freie Auflösungen äußerer Potenzen. Manuscripta Math 21, 341–355 (1977). https://doi.org/10.1007/BF01167853
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DOI: https://doi.org/10.1007/BF01167853