2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72837We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring $R$ and a reflexive $R$-module $M$ such that $\Ext^i_R(M,R)=0$ for all $i>0$, but $\Ext^i_R(M^*,R)\ne 0$ for all $i>0$.In the previous version, Proposition 2.1 is incorrect, as stated. We added the assumption "Artinian" in the statementCommutative Algebra13D07;13D02;13D25text