Let S be an arbitrary associative ring and S W 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 : MrarrDelta2 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 ldquocotilting conditionrdquo on finitely generated R-modules naturally arises.
Natural dualities
MANTESE, Francesca;
2004-01-01
Abstract
Let S be an arbitrary associative ring and S W 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 : MrarrDelta2 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 ldquocotilting conditionrdquo on finitely generated R-modules naturally arises.
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