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On Semiperfect Modules

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson
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Abstract

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Sandomierski (Proc. A.M.S. 21 (1969), 205–207) has proved that a ring is semiperfect if and only if every simple module has a projective cover. This is generalized to semiperfect modules as follows: If P is a projective module then P is semiperfect if and only if every simple homomorphic image of P has a projective cover and every proper submodule of P is contained in a maximal submodule.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 77 - 80
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bass, H., Finit is tic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488.Google Scholar
2. Golan, J. S., Quasiperfect Modules, Quart. J. Math. Oxford (2), 22 (1971), 173-82.Google Scholar
3. Kasch, F. and Mares, E. A., Eine Kennzeichnung Semi-perfecter Moduln, Nagoya Math. J. 27 (1966), 525-529.Google Scholar
4. Mares, E. A., Semiperfect modules, Math. Zeitschr. 82 (1963), 347-360.Google Scholar
5. Sandomierski, F. L., On semiperfect and perfect rings, Proc. Amer. Math. Soc. 21 (1969), 205-207.Google Scholar