2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168882We characterize the rings in which the equality $(τI:τ)= I^*$ holds for every ideal $I \subset R$. Under certain assumptions, these rings must be either weakly F-regular or one-dimensional.Commutative AlgebraWhen is tight closure determined by the test ideal?text