The noncommutative (Cohn) localization σR of a ring R is defined for any collection σ of morphisms of f.g. projective left R-modules. We exhibit σR as the endomorphism ring of R in an appropriate triangulated category. We use this expression to prove that if TorRi (σ R, σR) = 0 for i ≥ 1 then every bounded f.g. projective σR-module chain complex D with [D… (More)
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