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Topological Andr\'e-Quillen homology for commutative $S$-algebras wasintroduced by Basterra following work of Kriz, and has been intensively studiedby 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 andsimply connected spaces. We exhibit some new examples of minimal atomic$S$-algebras.

Topological Andr\'e-Quillen homology for cellular commutative $S$-algebras