2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70135We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a ``tantalizing question'' of Hochster.Some minor changes. To appear in Amer. J. of MathCommutative AlgebraAlgebraic Geometry13A35; 14H60text