Vector spaces are both projective and injective if the axiom of choice holds. Are there any other modules with this property? Do they have a good characterization?
Vector spaces are both projective and injective if the axiom of choice holds. Are there any other modules with this property? Do they have a good characterization?
there's a characterization of rings over which every module is both projective and injective. these rings are called semisimple and they are in the form where is any integer, each is a division ring and is the ring of matrices with entries in