2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62667Hara and Smith independently proved that in a normal $\mQ$-Gorenstein ring of characteristic $p \gg 0$, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair $(R, Δ)$ of a normal ring $R$ and an effective $\mQ$-Weil divisor $Δ$ on $\Spec R$. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.21 pages in AMS LaTeX, to appear in Journal of Algebraic GeometryAlgebraic GeometryCommutative Algebra13A35; 14B05text