Abstract
A right R-module M with endomorphism ring S is called a costar module if it induces the duality between the class of M R -torsionless right R-modules X with Hom R (X, M R ) finitely generated over S and the class of S M-torsionless finitely generated left S-modules. In this article we consider, more generally, a pair of additive, contravariant functors—which are adjoint on the right—between Grothendieck categories, and describe a natural duality induced by them. Our result subsumes the situation mentioned above but also, for example, a rigid graded duality that gives the notion of graded costar module.
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