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We discuss a class of modules, which we call $\underline{g}$-weak completeintersection modules, inspired by the weak complete intersection ideals studiedby Rahmati, Striuli, and Yang and we present explicit formulas for thegenerators of Koszul homology with coefficients in a $\underline{g}$-weakcomplete intersection module. This generalizes work of Herzog and of Corso,Goto, Huneke, Polini, and Ulrich. We use these explicit formulas to studyconnections between $\underline{g}$-weak complete intersection ideals and weakcomplete intersection ideals.

Generators of Koszul homology with coefficients in a $\underline{g}$-weak complete intersection module