2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/193823We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas for the purpose of obtaining the classical Rogers-Selberg recursions for the graded dimensions of the principal subspaces. This paper generalizes our previous paper.26 pages; v2: minor revisions, to appear in Journal of Pure and Applied AlgebraQuantum AlgebraHigh Energy Physics - TheoryRepresentation Theory17B69; 17B65text