Injective stabilization of additive functors. II. (Co)torsion and the Auslander-Gruson-Jensen functor (Q2286338)

In this paper, the second in a series of three, the authors define the torsion submodule of a module by using the injective stabilization of the tensor product with the module. If the underlying ring is a commutative domain, the torsion submodule coincides with the classical torsion submodule. Dually, by considering the projective stabilization of the Hom functor, the authors define the cotorsion quotient module of a module. They show some general properties of these two concepts. In particular, they consider the Auslander-Gruson-Jensen functor and its right adjoint and establish a duality between torsion and cotorsion over a ring with finitely presented injective envelope. The authors also present the derived functors of torsion and cotorsion under some finiteness conditions on the injective envelope of a ring. For Part I, see [the authors, ibid. 530, 429--469 (2019; Zbl 1444.16009)].