Dikranjan, D.; Orsatti, A. On linearly compact rings. (Italian) Zbl 0567.16028 Rend. Circ. Mat. Palermo, II. Ser., Suppl. 4, 59-74 (1984). The authors prove a representation theorem for a left linearly compact ring \((R,\tau)\) by constructing a ring \(A\) and a module \(U_ A\) such that \(R\) is isomorphic to \(\text{End}(U_ A)\) and the \(U\)-topology of \(R\) has the same closed left ideals as \((R,\tau)\). The proof is based on results of C. Menini [Rend. Semin. Mat. Univ. Padova 65, 251–262 (1981; Zbl 0483.16024)]. They also study the structure of the module \(U_ A\), giving as application simple proofs of classical theorems of Zelinsky and Leptin on the structure of linearly compact rings. Reviewer: José L. Gómez-Pardo (Santiago de Compostela) Cited in 1 Document MSC: 16W80 Topological and ordered rings and modules 16Dxx Modules, bimodules and ideals in associative algebras 16Gxx Representation theory of associative rings and algebras Keywords:representation theorem; left linearly compact ring Citations:Zbl 0483.16024 PDFBibTeX XMLCite \textit{D. Dikranjan} and \textit{A. Orsatti}, Suppl. Rend. Circ. Mat. Palermo (2) 4, 59--74 (1984; Zbl 0567.16028)