2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171603Given a noncommutative (Cohn) localization $A \to σ^{-1}A$ which is injective and stably flat we obtain a lifting theorem for induced f.g. projective $σ^{-1}A$-module chain complexes and localization exact sequences in algebraic $L$-theory, matching the algebraic $K$-theory localization exact sequence of Neeman and Ranicki.to appear in Advances in MathematicsAlgebraic TopologyRings and Algebras57A65; 19G24text