An introduction to constructive algebraic analysis and its applications
Alban Quadrat · Les cours du CIRM · 2010
If M and F are two left D-modules, then hom D (M, F) usually has an abelian group structure.Indeed, if hom D (M, F) has a left D-module structure defined by (d f )(m) = f (d m), for all d ∈ D and all m ∈ M , then, according to the definition of a left D-module, for all d, d ∈ D and for all f ∈ hom D (M, F), we have (d d ) f = d (d f ), and thus:But, f (d d m) and f (d d m) are not necessarily equal for all d, d ∈ D and all m ∈ M .(55)