Universal localization of triangular matrix rings

Abstract

If R R is a triangular 2 × 2 2\times 2 matrix ring, the columns P P and Q Q are f.g. projective R R -modules. We describe the universal localization of R R which makes invertible an R R -module morphism σ : P → Q \sigma :P\to Q , generalizing a theorem of A. Schofield. We also describe the universal localization of R R -modules.