Open AccessGeneralized Matlis duality
Author(s) -
Richard Belshoff,
Edgar E. Enochs,
J. R. García Rozas
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-05130-8
Subject(s) - algorithm , annotation , computer science , type (biology) , artificial intelligence , biology , ecology
Let R R be a commutative noetherian ring and let E E be the minimal injective cogenerator of the category of R R -modules. A module M M is said to be reflexive with respect to E E if the natural evaluation map from M M to Hom R ( Hom R ( M , E ) , E ) \operatorname {Hom}_R( \operatorname {Hom}_R(M,E), E) is an isomorphism. We give a classification of modules which are reflexive with respect to E E . A module M M is reflexive with respect to E E if and only if M M has a finitely generated submodule S S such that M / S M/S is artinian and R / ann ( M ) R/\operatorname {ann}(M) is a complete semi-local ring.