ABSTRACT
Given an exact complex F of free R modules, we seek ideals H in R which have the following property. If C is another complex of free R modules, then any isomorphism ϕ : C ⊗ R / H → F ⊗ R / H of R module lifts up to radical to an isomorphism from C to F. We show that for finite complexes F a power of the first fitting ideal I (f 1) is one such ideal. In some cases we show that up to radical this is the largest possible ideal. Whether I ( f 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187902/c5c94f90-3607-4522-9781-6827dcae56e6/content/in12_u001.tif"/> is the largest possible ideal in general is still open.
