Topological Morita equivalences induced by ideals generated by dense idempotents
An idempotent \(e\) of a topological ring \(R\) is called dense provided \(ReR\) is a dense ideal in \(R\). Let \(R\) be a complete right linearly topologized ring and \(e\) a dense idempotent of it. A pair of functors is indicated which realizes the equivalence between the category of complete linearly topologized right \(R\)-modules and complete linearly topologized right \(eRe\)-modules. The main result of the paper is applied in order to get a result of \textit{Y. Xu, K.-P. Shum}, and \textit{R. F. Turner-Smith} [J. Algebra 159, No. 2, 425-435 (1993; Zbl 0816.16007)].
scientific article; zbMATH DE number 1211659