Dubrovin valuation rings and Henselization (Q1101531)

This paper develops the theory of a class of valuation rings for tensions of M, and the torsion-theoretical localizations of M are examined. For example, if every pair of modules \(N\subseteq E(N)\) satisfies (1), then R is semisimple; if \(0\neq N\subseteq E(M)\) satisfies (1), then N has a unique maximal extension in M and M satisfies (2); and if N is \(\tau\)- torsionfree for some torsion theory \(\tau\), then \(N\subseteq Q_{\tau}(N)\) satisfies (1), where \(Q_{\tau}(N)\) denotes the localization of N with respect to \(\tau\).