Characterizing rings in terms of the extent of the injectivity of their simple modules (Q6159764)

The authors offer a very precise and systematic study of the nature of a ring in terms of its simple modules. It is given in particular a classification of rings with certain types of simple modules (injective, poor or indigent). Artinian and Noetherian rings are considered as those being part of a decomposition in terms of a cartesian product. Some interesting examples from the literature are given to illustrate the main results (graph magma algebras in particular).