2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72044If R is a triangular 2x2 matrix ring, the columns, P and Q, are projective left R-modules. We describe the universal localization of R which makes invertible an R-module morphism P --> Q, generalizing a theorem of A.Schofield. We also describe the universal localization of R-modules.Author died in March 2005. Revised version prepared by Andrew Ranicki with the assistance of Aidan Schofield. To appear in the Proceedings of the AMSRings and Algebras16S10; 16S50text