2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74073It is shown that tight closure commutes with localization in any two dimensional ring $R$ of prime characteristic if either $R$ is a Nagata ring or $R$ possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals in any ring of prime characteristic.7 pages, to appear in Proc. Indian Acad. Sci. (Math. Sci.)Commutative Algebra13A35, 13C99text