Left noetherian rings are exactly those whose modules form a superstable class with embeddings, and left pure-semisimple rings are exactly those whose modules form a superstable class with pure embeddings.
[Sim00] Daniel Simson, An Artin problem for division ring extensions and the pure se misimplicity conjecture
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Superstability, noetherian rings and pure-semisimple rings
Left noetherian rings are exactly those whose modules form a superstable class with embeddings, and left pure-semisimple rings are exactly those whose modules form a superstable class with pure embeddings.