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On completely principally injective rings

Published online by Cambridge University Press:  17 April 2009

W.K. Nicholson  and
M.F. Yousif
W.K. Nicholson
Affiliation:
Department of MathematicsUniversity of CalgaryCalgary, AlbertaCanadaT2N 1N4
M.F. Yousif
Affiliation:
Department of MathematicsThe Ohio State University at Lima4240 Campus Drive Lima OH 45804United States of America
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A ring R is called right principally injective (right P-injective) if every R-linear map from a principal right ideal of R can be extended to R. If every ring homomorphic image of R is right P-injective, R is called completely right P-injective (right CP-injective). In this paper we characterise completely quasi-Frobenius rings in terms of CP-injectivity.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 513 - 518
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Beachy, J.A., ‘On quasi-artinian rings’, J. London Math. Soc. 3 (1971), 449–452.CrossRefGoogle Scholar
[2]Camillo, V., ‘Commutative rings whose principal ideals are annihilators’, Portugal. Math. 46 (1989), 33–37.Google Scholar
[3]Faith, C., Algebra II, Ring theory (Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[4]Gordon, R. and Robson, J.C., ‘Krull dimension’, Mem. Amer. Math. Soc. 133 (1973).Google Scholar
[5]Harada, M., ‘On modules with extending properties’, Osaka J. Math. 19 (1982), 203–215.Google Scholar
[6]Kasch, F., Modules and rings, London. Math. Soc. Monographs 17 (Academic Press, New York, 1982).Google Scholar
[7]Mohamed, S.H. and Müller, B.J., Continuous and discrete modules, London Math. Soc. Lecture Notes Series 147 (Cambridge University Press, Oxford, 1990).CrossRefGoogle Scholar
[8]Nicholson, W.K. and Yousif, M.R., ‘Principally injective rings’, J. Algebra (to appear).Google Scholar
[9]Shock, R.C., ‘Dual generalizations of the artinian and neotherian conditions’, Pacific J. Math. 54 (1974), 227–235.CrossRefGoogle Scholar