Abstract We uncover a connection between the model-theoretic notion of superstability and that noetherian rings pure-semisimple rings. characterize via class left modules with embeddings. Theorem 0.1 For ring R following are equivalent. (1) is noetherian. (2) The R-modules embeddings superstable. (3) every ? ? | + ? 0 , there ? such has uniqueness limit models cardinality ?. (4) Every model in ...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...