Injective modules and torsion functors* |
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| Authors: | Pham Hung Quy |
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| Institution: | Department of Mathematics, FPT University, Hanoi, Vietnam |
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| Abstract: | A commutative ring is said to have ITI with respect to an ideal 𝔞 if the 𝔞-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. |
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| Keywords: | Injective module ITI local cohomology non-noetherian ring torsion functor weakly proregular ideal |
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