2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116476Over an associative ring we consider a class $\mathbb{X}$ of left modules which is closed under set-indexed coproducts and direct summands. We investigate when the triangulated homotopy category $\mathsf{K}(\mathbb{X})$ is compactly generated, and give a number of examples.20 pagesCommutative Algebra16D20, 16D40, 16D50, 16D90, 16E05text