Topological Morita Equivalences Induced by Ideals Generated by Dense Idempotents
✍ Scribed by G Mezzetti
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 261 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Given two complete right linearly topologized rings R, and S, , and a Ž . bimodule B endowed with a complete topology , in such a way that B ,  g R S S Ž . Ž . u Ž . CLT-S, and there be a continuous ring homomorphism R, ª CEnd B,  , S ˆŽ . Ž . we define a functor ym B: CLT-R, ª CLT-S, which is left adjoint to the R u ŽŽ . . Ž . Ž . functor CHom B,  , y : CLT-S, ª CLT-R, . Then we consider the par-S Ž . ticular case in which S, s eRe with its induced topology, where e is a dense Ž Ž . . idempotent of R that is, ReR is dense in R, . Under these hypotheses we show ˆŽ . Ž . that the pair of functors ym Re: CLT-R, ª CLT-S, and ym eR: CLT-R S Ž .
Ž . S, ªCLT-R, is an equivalence of categories. As an application of this result, we re-obtain a theorem of Xu, Shum, and Turner-Smith on similarities between infinite matrix subrings.