Linearly compact modules over HNP rings (Q1064391)

Let R be a hereditary noetherian prime ring (an HNP ring), A a maximal invertible ideal of R. By \(F_ A\) is denoted the right Gabriel topology with the base of neighbourhoods of 0 consisting of all right ideals containing some power of A and by \(\hat R\) the completion of R with respect to this topology. The author gives a full description of linearly compact \(\hat R-\)modules. They are just the products of modules of the following four types: (I) \(e_ i\hat R/e_ i\hat A^ n\), \(n=1,2,...\), where \(\hat A=\hat RA\), \(i=1,...,p\), p a positive integer, \(\{e_ 1,...,e_ p\}^ a \)system of orthogonal idempotents of \(\hat R;\) (II) \(E(e_ i\hat R/e_ i\hat A)\), \(i=1,...,p\), where \(E(e_ i\hat R/e_ i\hat A)\) is the injective hull of \(e_ i\hat R/e_ i\hat A\); (III) \(e_ i\hat R\), \(i=1,...,p\); (IV) \(e_ i\hat Q\), where \(\hat Q\) is the quotient ring of \(\hat R,\) \(i=1,...,p\).