Morita duality for rings with local units
Using an appropriate generalization of the notion of discrete linearly compact modules over a ring with identity, the authors achieve deeper results about the structure of rings with local units and with Morita duality. The main result translates that of \textit{B. J. Müller} [Math. Z. 119, 63-74 (1971; Zbl 0198.059)] to rings with local units: a ring \(R\) with local units has a Morita duality if and only if \(R\) is discrete linearly compact and injective hulls of simple \(R\)-modules are discrete linearly compact, and an \(R\)-module is reflexive if and only if it is discrete linearly compact. \(R\) has a Morita duality if and only if \(eRe\) has a Morita duality for each \(e^ 2 = e\in R\). If \(R\) is also commutative, then \(R\) has a Morita duality if and only if \(R\) is discrete linearly compact if and only if \(R\) is a (not necessarily finite) direct sum of discrete linearly compact rings with identity.
scientific article; zbMATH DE number 579543