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Modules Over Hereditary Noetherian Prime Rings, II

  • Surjeet Singh (a1)

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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)).

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References

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1. Eisenbud, D. and Griffith, P., Serial rings, J. Algebra 17 (1971), 389400.
2. Eisenbud, D. and Robson, J. C., Modules over Dedekind prime rings, J. Algebra 16 (1970), 6784.
3. Eisenbud, D. and Robson, J. C., Hereditary noeiherian prime rings, J. Algebra 16 (1970), 86101.
4. Fuchs, L., Abelian groups (Pergamon Press, 1960).
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7. Kuzamanovitch, J., Localizations of Dedekind prime rings, J. Algebra 21 (1972), 371393.
8. Lenagan, T. H., Bounded hereditary noeiherian prime rings, J. London Math. Soc. 6 (1973), 241246.
9. Marubayashi, H., Modules over bounded Dedekind prime rings, Osaka J. Math. 9 (1972), 95110.
10. Singh, S., Quasi-injective and quasi-projective modules over hereditary noeiherian prime rings, Can. J. Math. 26 (1974), 11731185.
11. Singh, S., Modules over hereditary noeiherian prime rings, Can. J. Math. 27 (1975), 867883.
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Modules Over Hereditary Noetherian Prime Rings, II

  • Surjeet Singh (a1)

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