Generalized Matlis duality, on a Noetherian commutative ring - Mendoza Quispe, Wilfredo (2024)
Let R be a Noetherian commutative ring and let E be the minimal injective cogenerator of the category of R-modules. Belshoff, Enochs and García Rozas are three people who introduced in [6] the so-called I-reflexive Matlis modules where I is an ideal. In this context we present in the second section a brief introduction of the reflective modules and some of their properties, and in the third and last section we give the classification of reflective modules with respect to a minimal cogenerator E. A node M is said to be reflexive with respect to E if the map of M in Hom(HomR(M, E), E) is an isomorphism and thus we establish the classification of the R-modules M, which are reflexive with respect to E if and only if M has a finitely generated submodule S such that the quotients: M/S and R/anul(M) is complete Artinian and semilocal respectively.