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On linearly compact rings. (Italian) Zbl 0567.16028

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.

MSC:

16W80 Topological and ordered rings and modules
16Dxx Modules, bimodules and ideals in associative algebras
16Gxx Representation theory of associative rings and algebras

Citations:

Zbl 0483.16024
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