Essentially compressible modules and rings.
Let \(R\) be a ring with identity element. A unital right \(R\)-module \(M\) is called `essentially compressible' if \(M\) embeds in every essential submodule of \(M\). The ring \(R\) is said to be `right essentially compressible' if the right module \(R_R\) is essentially compressible. The aim of this paper is a study of essentially compressible modules and rings. Thus, the authors prove that every non-singular essentially compressible \(R\)-module is isomorphic to a submodule of a free \(R\)-module, and the converse holds if \(R\) is semiprime right Goldie. In case \(R\) is a right FBN ring, it is shown that a right \(R\)-module \(M\) is essentially compressible if and only if \(M\) embeds in a direct sum of critical compressible right \(R\)-modules. Then, the authors characterize the right essentially compressible rings, and as a consequence, it follows that \(R\) is semiprime right Goldie if and only if \(R\) is a right essentially compressible ring having at least one uniform right ideal.
scientific article; zbMATH DE number 5077823