Cotilting duality: a functorial approach
by
Alberto Tonolo
Dipartimento di Matematica Pura ed Applicata - Universitá di Padova

Let R and S be arbitrary associative rings. A faithfully balanced bimodule _SU_R is said to be a cotilting bimodule if both Cogen(U_R) = KerExt 1R-U and Cogen(_SU) = KerExt 1S-U hold. We denote by \Delta_? and \Gamma_? the functors Hom_?(-, _SU_R) and Ext 1?-_SU_R, where ? = R or S. The bimodule _SU_R cogenerates torsion theories in \rmod R and S\lmod. As in the Morita case, one of the main problems for cotilting dualities is to find out the largest classes of R and S-modules where a torsion theory duality works. While the notion of \Delta_?-reflexive modules is easily defined through the evaluation map, the main point is to recognize the class of \Gamma_?-reflexive modules. We are able to define in a functorial way such classes, realizing for them a dual version of the Brenner and Butler Theorem. This functorial approach continues the theory developed on the the paper , and to which we are deeply indebted.

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R.Colpi, Cotilting bimodules and their dualities, preprint.

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R.Colpi, K.Fuller, Cotilting modules and bimodules, to appear in Pacific J. Math.

Date received: February 1, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-62.