2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158282The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)is studied. It is proved that over generic R every M has a Koszul syzygy module. Explicit families of Koszul modules are identified. When R is Gorenstein the non-Koszul modules are classified. Structure theorems are established for the graded k-algebra Ext_R(k,k) and its graded module Ext_R(M,k).17 pages; number of minor changes. This article will appear in the Journal of the London Math. SocCommutative Algebra13D02 (Primary), 13D07 (Secondary)text