2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66722Let $(R, \m)$ be a commutative Noetherian local ring with $\m^3 =(0)$. We give a condition for $R$ to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over $R$ is not necessarily a contravariantly finite subcategory in the category of finitely generated $R$-modules.20 pagesCommutative Algebra13C14, 13D05, 16G50text