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Quasi-Injective and Pseudo-Infective Modules

  • S. K. Jain (a1) and Surjeet Singh (a1)

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Let R be a ring with identity not equal to zero. A right R-module is said to be quasi-injective (pseudo-injective) if for every submodule N of M, every R-homomorphism (R-monomorphism) of N into M can be extended to an R-endomorphism of M [7] ([13]).

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References

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1. Eisenbud, D. and Griffith, P., Serial rings, J. Algebra 17 (1971), 389-400.
2. Eisenbud, D. and Robson, J. C., Hereditary noetherian prime rings, J. Algebra 16 (1970), 86-104.
3. Faith, C., Lectures on injective modules and quotient rings, Lecture Notes in Math., No. 49 (1967), Springer-Verlag.
4. Hallett, R. R., Injective modules and their generalizations, Ph.D. thesis, Univ. of British Columbia, Vancouver, Dec. 1971.
5. Harada, M., Note on quasi-injective modules, Osaka J. Math. 2 (1965), 351-356.
6. Johnson, R. E., Quotient rings of rings with zero singular ideal, Pacific J. Math. 11 (1961), 1385-1392.
7. Johnson, R. E. and Wong, E. T., Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260-268.
8. Lenagan, T. H., Bounded hereditary noetherian prime rings, J. London Math. Soc. 6 (1973), 241-246.
9. Levy, L., Torsion free and divisible modules over non-integral domains, Canadian J. Math. 15 (1963), 132-151.
10. Matlis, E., Injective modules over noetherian rings, Pacific J. Math. 8 (1958), 511-528.
11. McConnell, J. C. and Robson, J. C., Homomorphisms and extensions of modules over certain differential polynomial rings, J. Algebra 26 (1973), 319-342.
12. Nakayama, T., On Frobeniusean algebras II, Ann. Math. (2) 42 (1941), 1-21.
13. Singh, S. and Jain, S. K., On pseudo-injective modules and self pseudo-injective rings, J. Math. Sci. 2(1967), 23-31.
14. Singh, S., On pseudo-injective modules, Rivisto. Mat. Univ. Parma, 9 (1968), 59-65.
15. Singh, S. and Wason, K., Pseudo-injective modules over commutative rings, J. Indian Math. Soc. 34 (1970), 61-66.
16. Singh, S., Quasi-injective and quasi-projective modules over hereditary noetherian prime rings, Canadian J. Math, (to appear).
17. Teply, M. L., Private communication.
18. Teply, M. L., Pseudo-injective modules which are not quasi-injective, Proc. Amer. Math. Soc. (to appear).
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Quasi-Injective and Pseudo-Infective Modules

  • S. K. Jain (a1) and Surjeet Singh (a1)

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