2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/197760This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.20 pages. To appear in International J. of MathQuantum AlgebraHigh Energy Physics - TheoryRepresentation Theory17B69; 17B65; 05A17text