2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97237This paper gives an elementary introduction to noncommutative deformations of modules. The main results of this deformation theory are due to Laudal. Let k be an algebraically closed (commutative) field, let A be an associative k-algebra, and let M = {M_1, ..., M_p} be a finite family of left A-modules. We study the simultaneous formal deformations of the family M, described by the noncommutative deformation functor Def(M): a(p) -> Sets introduced by Laudal. In particular, we prove that the deformation functor Def(M) has a pro-representing hull H(M), unique up to non-canonical isomorphism, and describe how to calculate H(M) using the Ext groups of the family M and their matric Massey products.33 pages, AMS-LaTeX, uses package Xy-pic, submitted to Noncommutative Geometry and Rings (Almeria 2002) conference proceedingsAlgebraic GeometryRings and AlgebrasRepresentation Theory14D15; 14B12text