Abstract
We introduce a class of modules, called J-closed modules, inspired by the weak complete intersection ideals studied by Rahmati, Striuli, and Yang. We present explicit formulas for the generators of Koszul homology with coefficients in such modules. This generalizes work of Herzog and of Corso, Goto, Huneke, Polini, and Ulrich. We use these formulas to study connections between J-closed ideals and weak complete intersection ideals.
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