Divisibility and duo-rings
Let \(R\) be a right non-singular ring with maximal right ring of quotients \(Q\). This paper addresses the question of when the projective dimension pd\(_R(Q)\leq 1\) implies that \(Q/R\) is a direct sum of countable modules. That property allows several notions in the literature of divisibility concerning modules over integral domains to be extended to the non-commutative case. For example, the authors study the relations between the following properties of a module \(D\): \begin{itemize} \item for all regular \(c\in R,\ Dc=D\); \item \(D\) is the epimorphic image of an injective module; \item for all \(r\in R,\ \mathrm{Ext}_R^1(R/rR,\, D)=0\). \end{itemize}
scientific article; zbMATH DE number 7219813
scientific article