Injective modules and torsion functors
Pham Hung Quy, Fred Rohrer
TL;DR
This paper investigates the properties of injective modules and torsion functors in commutative rings, exploring conditions for ITI, its behavior under various ring constructions, and applications to local cohomology in non-noetherian contexts.
Contribution
It characterizes rings with ITI, analyzes how ITI behaves under ring operations, and applies findings to local cohomology over non-noetherian rings.
Findings
Identification of classes of rings with or without ITI
Behavior of ITI under ring fractions, tensor products, and idealisation
Applications to local cohomology in non-noetherian rings
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. Behaviour of ITI under formation of rings of fractions, tensor products and idealisation is studied. Applications to local cohomology over non-noetherian rings are given.
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