Injective modules and torsion functors

摘要

A commutative ring is said to have ITI with respect to an ideal ? if the ?-torsion functor preserves injectivity of modules. Classes of rings with ITI or without ITI with respect to certain sets of ideals are identified. Behavior of ITI under formation of rings of fractions, tensor products, and idealization is studied. Applications to local cohomology over non-noetherian rings are given.