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Decomposition Theorems for q*-Rings

Published online by Cambridge University Press:  20 November 2018

David A. Hill
David A. Hill*
Affiliation:
Instituto de Matematica Universidade Federal da Bahia Salvador, BahiaBrasil
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Let R be a ring with identity. The study of rings in which every left (right) ideal is quasi-injective was begun by Jain, Mohamed, and Singh (3). They called these rings left (right) q-rings. A number of structure theorems have been proved for q-rings. See, for example, (1), (2), and (5). A ring with the dual property (rings in which every homomorphic image of R as a left (right) R-module is quasi-projective) is called left (right) q*. These rings were first studied by Koehler (4), where some results connecting q* -rings with q-rings were obtained.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 2 , 01 June 1980 , pp. 155 - 160
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Hill, D. A., Semi-perfect q-rings. Math. Ann. 200, 113-121 (1973).Google Scholar
2. Ivanov, G., Non-local rings whose ideals are all quasi-injective. Bull. Austral. Math. Soc. 6, 45-52 (1972).Google Scholar
3. Jain, S. K., Mohamed, S. H., Singh, S., Rings in which every right ideal is quasi-injective. Pacific J. Math. 31, 73-79 (1969).Google Scholar
4. Koehler, A., Rings for which every cyclic module is quasi-projective. Math. Ann. 189, 311-316 (1970).Google Scholar
5. Mohamed, S. H., q-Rings with chain conditions. J. London Math. Soc. (2), 2, 455-460 (1970).Google Scholar
6. Robert, E., Projectifs et injectifs relatifs. C.R. Acad. Sci. Paris Ser. A., 268, 361-364 (1969).Google Scholar