The canonical topology of FBN maximal orders (Q1209740)

Let \(R\) be a fully bounded noetherian prime ring which is a maximal order in its classical ring of quotients \(Q\). The canonical topology \(\tau\) of \(R\) is given by the hereditary torsion theory cogenerated by \(Q\oplus E(Q/R)\). The author shows for a \(\tau\)-torsion \(R\)-module \(M\), that its (finite) Krull-dimension \(\dim M\leq (\dim R)-2\). The converse is proved under the assumption that the height-one prime ideals \(P\) of \(R\) are characterized by the property \(\dim(R/P) = (\dim R)-1\). Furthermore, the stability of \(\tau\) is shown.