Geodesic
A Type of Quasi-Frobenius Ring
Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 19-27

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In [3], the author proved that a ring R with identity is right noetherian and right injective if and only if R is a direct sum of a finite number of uniform right ideals, which are completely primary in the sense of that paper. In this paper, we shall determine the structure of such rings in the case where the sum of the isomorphic uniform components are twosided ideals. The ring is found to be a direct sum of total matrix rings over local rings. 
Feller, Edmund H. A Type of Quasi-Frobenius Ring. Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 19-27. doi: 10.4153/CMB-1967-003-4
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