Principally quasi-injective modules. (English) Zbl 0924.16004

The paper deals with properties and characterizations of principally quasi-injective \(R\)-modules, i.e., modules for which each \(R\)-homomorphism from a principal submodule of \(M\) to \(M\) can be extended to an endomorphism of \(M\). This is a generalization of both quasi-injective modules and principally injective modules. Many of the properties of these two classes of modules are extended to principally quasi-injective modules. Properties covered include those relating to the Jacobson radical, the endomorphism ring and uniform submodules.


16D50 Injective modules, self-injective associative rings
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