Geodesic
On a Class of Perfect Rings
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 822-826

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

In [3], the perfect rings of Bass [1] were characterized in terms of torsions in the following way: A ring R is right perfect if and only if every (hereditary) torsion in the categoryMod Rof all left R-modules is fundamental (i.e. generated by some minimal torsions) and closed under taking direct products; as a consequence, the number of all torsions inMod Ris finite and equal to 2n for a natural n.Here, we present a simple description of those rings R which allow only two (trivial) torsions, viz. 0 and Mod R (and thus, are right perfect by [3]). Finite direct sums of these rings represent a natural generalization of completely reducible (i.e. artinian semisimple) rings (cf. Theorem 2) and we shall call them for that matter π-reducible rings. They can also be characterized in terms of their idempotent two-sided ideals. 
Dlab, Vlastimil. On a Class of Perfect Rings. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 822-826. doi: 10.4153/CJM-1970-092-1
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[1] 1. Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. Google Scholar

[2] 2. Courter, R., Finite direct sums of complete matrix rings over perfect completely primary rings, Can. J. Math. 21 (1969), 430–446. Google Scholar

[3] 3. Dlab, V., A characterization of perfect rings, Pacific J. Math. 83 (1970), 79–88. Google Scholar

[4] 4. Findlay, G. D. and Lambek, J., A generalized ring of quotients. I, II, Can. Math. Bull. 1 (1958), 77-85, 155–167. Google Scholar

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