We will complete the proof of the Shamash construction which uses the system of higher homotopies for a Q-projective resolution to construct an R-resolution of an R -module M over R = Q/(f), where f is non-zero divisor. We will derive consequences for periodicity of minimal free resolutions when F. is a finite complex of free Q-modules and Q is a Noetherian local ring. Time permitting, we will examine the connections with matrix factorisations and some generalisations of the construction due to Eisen bud.
