Geodesic
Ring Theoretic Properties of Matrix Rings
Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 365-374

Voir la notice de l'article provenant de la source Cambridge University Press

K. Morita has shown that, given two rings R and S, there is an isomorphism between the category of left R-modules and the category of left S-modules if and only if there exists an R-S bimodule U such that(1) U is a progenerator in the category of left R-modules, and(2) S ≅ (EndR U)opp as rings. 
Kaye, S.M. Ring Theoretic Properties of Matrix Rings. Canadian mathematical bulletin, Tome 10 (1967) no. 3, pp. 365-374. doi: 10.4153/CMB-1967-034-3
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