Geodesic
On the idempotence and stability of kernel functors
Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 37-43

Voir la notice de l'article provenant de la source Cambridge University Press

A kernel functor (equivalently, a left exact torsion preradical) is a left exact subfunctor of the identity on the category R-mod of left R-modules over a ring R with identity. A kernel functor is said to be idempotent if, in addition, σ satisfies σ(M / σ(M)) = 0 for every M ∊ R-mod. To every kernel functor / there corresponds a unique topologizing filter Lσ = {I I σ (R/I) = R/I} of left ideals and a unique class Fσ = {M ∊ R-mod I σ(M) = M} that is closed under homomorphic images, submodules, and direct sums. The idempotence of σ is characterized by either of the following additional conditions:(1) if I ∊ Lσ, K ⊆ I, and (K:x) = {r ∊ R ∣ rx ∊ K} ∊ Lσ for each x ∊ I, then K ∊ L or(2) Fσ is closed under extensions of one member of Fσ by another member of Fσ Idempotent kernel functors are important since they are the tool used to construct localization functors. For M∊ R-mod, let E(M) denote the injective hull of M. A kernel functor σ is called stable if MF implies that E(M) ∊ Fσ For more information about kernel functors, see [6], [7], [14], and [15]. 
Teply, Mark L. On the idempotence and stability of kernel functors. Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 37-43. doi: 10.1017/S0017089500030366
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