Natural Dualities
by Mantese, Francesca; Tonolo, Alberto
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 Δ both the contravariant functors Hom
S
(−,W) and Hom
R
(−,W). A module M is reflexive if the evaluation map δ
M
: M→Δ2
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.
DOI: 10.1023/B:ALGE.0000019385.66745.59
Print publication date: 3/1/2004
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