Let S be an arbitrary associative ring and SW be a left S-module. Denote by R the ring End(S) W and by Delta both the contravariant functors Hom(S)(-, W) and Hom(R)(-, W). A module M is reflexive if the evaluation map delta(M): M --> Delta(2)M is an isomorphism. Any direct summand of finite direct sums of copies of (S)W and of R(R) is reflexive. Increasing in a minimal way the classes of reflexive modules, a "cotilting condition" on finitely generated R-modules naturally arises.
Natural dualities
TONOLO, ALBERTO
2004
Abstract
Let S be an arbitrary associative ring and SW be a left S-module. Denote by R the ring End(S) W and by Delta both the contravariant functors Hom(S)(-, W) and Hom(R)(-, W). A module M is reflexive if the evaluation map delta(M): M --> Delta(2)M is an isomorphism. Any direct summand of finite direct sums of copies of (S)W and of R(R) is reflexive. Increasing in a minimal way the classes of reflexive modules, a "cotilting condition" on finitely generated R-modules naturally arises.
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