A characterization of rings with Krull dimension
Many classes of rings can be, and have been, characterized by their cyclic modules. The present authors continue this line of investigation by considering rings with Krull dimension. They consider the following property: (P). Every cyclic right R-module is a direct sum of an injective module and a module containing an essential submodule with Krull dimension at most \(\alpha\). The main result is that a ring with property (P) has right Krull dimension at most \(\alpha\).
scientific article; zbMATH DE number 4158878
scientific article