Annihilating complexes of modules
Dmitri Apassov · MATHEMATICA SCANDINAVICA · 1999
For a complex X of modules over a commutative ring R the weak annihilator is defined by Ann R XiPZ Ann R H i X , the intersection of the annihilators of the homology modules, homotopy annihilator hann R X as the kernel of the map R 3 H 0 Hom R X Y X, and when X is homologically bounded, say H i X 0 for jij b n, the small annihilator is ann R X Ann R H Àn X Á Á Á Ann R H n X, the product of the annihilators of the homology modules.Various properties of annihilators are investigated; in particular it is proved that for suitably bounded complexes X and Y the homotopy annihilator hann R X is contained in hann R Hom R X Y Y and hann R X v R Y .