On semiperfect and perfect rings. (English) Zbl 0184.06402
The author proves that a ring \(R\) is semiperfect if and only if every simple right \(R\)-module has a projective cover. This is a generalization of a reviewer’s result in a commutative case [Proc. Am. Math. Soc. 19, 205–208 (1968; Zbl 0155.07402)].
Reviewer: Kwangil Koh (Raleigh)
MSC:
| 16L30 | Noncommutative local and semilocal rings, perfect rings |
Citations:
Zbl 0155.07402References:
| [1] | Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466 – 488. · Zbl 0094.02201 |
| [2] | Kwangil Koh, On a semiprimary ring, Proc. Amer. Math. Soc. 19 (1968), 205 – 208. · Zbl 0155.07402 |
| [3] | Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. · Zbl 0365.16001 |
| [4] | Bodo Pareigis, Radikale und kleine Moduln, Bayer. Akad. Wiss. Math.-Natur. Kl. S.-B. 1965 (1966), no. Abt. II, 185 – 199 (1966) (German). · Zbl 0207.32703 |
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