2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166564Topological André-Quillen homology for commutative $S$-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this paper we discuss it as a homology theory on CW $S$-algebras and apply it to obtain results on minimal atomic $p$-local $S$-algebras which generalise those of Baker and May for $p$-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic $S$-algebras.Final revision, a version will appear in Abhandlungen aus dem Mathematischen Seminar der Universitaet HamburgAlgebraic TopologyK-Theory and Homology55P43 (Primary); 13D03, 55N35, 55P48 (Secondary)text