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Modules Over Hereditary Noetherian Prime Rings, II

Published online by Cambridge University Press:  20 November 2018

Surjeet Singh
Surjeet Singh*
Affiliation:
Guru Nanak Dev University, Amritsar, India
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Let R be a hereditary noetherian prime ring ((hnp)-ring) with enough invertible ideals. Torsion modules over bounded (hnp)-rings were studied by the author in [10; 11]. All the results proved in [10; 11] also hold for torsion R-modules having no completely faithful submodules. In Section 2, indecomposable injective torsion R-modules which are not completely faithful are studied, and they are shown to have finite periodicities (Theorem (2.8) and Corollary (2.9)). These results are used to determine the structure of quasi-injective and quasi-projective modules over bounded (hnp)-rings (Theorems (2.13), (2.14) and (2.15)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 73 - 82
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Eisenbud, D. and Griffith, P., Serial rings, J. Algebra 17 (1971), 389–400.Google Scholar
2. Eisenbud, D. and Robson, J. C., Modules over Dedekind prime rings, J. Algebra 16 (1970), 67–84.Google Scholar
3. Eisenbud, D. and Robson, J. C., Hereditary noeiherian prime rings, J. Algebra 16 (1970), 86–101.Google Scholar
4. Fuchs, L., Abelian groups (Pergamon Press, 1960).Google Scholar
5. Goldie, A. W., Semi prime rings with maximum conditions, Proc. London Math. Soc. 10 (1960), 201–220.Google Scholar
6. Kuzamanovitch, J., Completions of Dedekind prime rings as second endomorphism rings, Pacific J. Math. 86 (1971), 721–729.Google Scholar
7. Kuzamanovitch, J., Localizations of Dedekind prime rings, J. Algebra 21 (1972), 371–393.Google Scholar
8. Lenagan, T. H., Bounded hereditary noeiherian prime rings, J. London Math. Soc. 6 (1973), 241–246.Google Scholar
9. Marubayashi, H., Modules over bounded Dedekind prime rings, Osaka J. Math. 9 (1972), 95–110.Google Scholar
10. Singh, S., Quasi-injective and quasi-projective modules over hereditary noeiherian prime rings, Can. J. Math. 26 (1974), 1173–1185.Google Scholar
11. Singh, S., Modules over hereditary noeiherian prime rings, Can. J. Math. 27 (1975), 867–883.Google Scholar