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Quasi-Injective and Quasi-Projective Modules Over Hereditary Noetherian Prime Rings

Published online by Cambridge University Press:  20 November 2018

Surjeet Singh
Surjeet Singh*
Affiliation:
Aligarh Muslim University, Aligarh, U.P. (India)
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The structure theory of hereditary noetherian prime (hnp) rings—in particular of Dedekind prime rings—has been recently developed by many authors including Eisenbud, Griffith, Michler and Robson; this theory extends some of the well-known results concerning commutative Dedekind domains. In this paper we study quasi-injective modules and quasi-projective modules over those (hnp) rings which are not right primitive and establish some results which extend the corresponding well-known results concerning commutative Dedekind domains. Let R be an (hnp) ring, which is not right primitive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1173 - 1185
Copyright
Copyright © Canadian Mathematical Society 1974

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), 67–85.Google Scholar
3. Eisenbud, D. and Robson, J. C., Hereditary noetherian prime rings, J. Algebra 16 (1970), 86–104.Google Scholar
4. Faith, C. and Utumi, Y., Quasi injective modules and their endomorphism rings, Arch. Math. 15 (1964), 166–174.Google Scholar
5. Fuller, K. R., Generalized uniserial rings and their Kupisch series, Math. Z. 106 (1968), 248–260.Google Scholar
6. Golan, J. S., Characterizations of rings using quasi projective modules. II, Proc. Amer. Math. Soc. 28 (1971), 337–343.Google Scholar
7. Goldie, A. W., The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. 8 (1958), 589–608.Google Scholar
8. Jacobson, N., The theory of rings, Mathematical Survey II (Amer. Math. Soc, Providence, 1943).Google Scholar
9. Johnson, R. E. and Wong, E. T., Quasi infective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260–264.Google Scholar
10. Kupisch, H., Beitrage Zür Théorie nichtalbeinfacher Ringe mit minimal Bedingung, Crell J. 201 (1959), 100–112.Google Scholar
11. Matlis, E., Infective modules over noetherian rings, Pacific J. Math. 8 (1958), 511–528.Google Scholar
12. Michler, G. O., Characterisierung einer Klasse von Noetherschen Ringen, Math. Z. 100 (1967), 163–182.Google Scholar
13. Michlet, G. O., Structure of semi-perfect hereditary noetherian ring, J. Algebra 13 (1969), 327–344.Google Scholar
14. Miyashita, , On quazi infective modules, J. Fac. Sci. Hokkaido Univ. Ser. I 18 (1965), 158–187.Google Scholar
15. Murase, I., On the structure of generalized uniserial rings. I, Sci. Papers College Gen. Ed. Univ. Tokyo 13 (1963), 1–22.Google Scholar
16. Murase, I., On the structure of generalized uniserial rings, II, Sci. Papers College Gen. Ed. Tokyo 13 (1963), 131–158.Google Scholar
17. Murase, I., On the structure of generalized uniserial rings, III, Sci. Pap. Coll. Gen. Edu. Univ. Tokyo 14 (1964), 11–25.Google Scholar
18. Rangaswamy, K. M. and Vanaja, Quasi projectives in abelian categories, Pacific J. Math. 43 (1972) (to appear).Google Scholar
19. deRobert, E., Projectifs et injectifs, applications, C. R. Acad. Sci. Paris Ser. A-B 268 (1969), 361–364.Google Scholar
20. Wu, L. E. T. and Jans, J. P., On quasi projectives, Illinois. J. Math. 11 (1967), 439–447.Google Scholar