Geodesic
Quasi-Injective and Pseudo-Infective Modules
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 359-366

Voir la notice de l'article provenant de la source Cambridge University Press

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]). 
Jain, S. K.; Singh, Surjeet. Quasi-Injective and Pseudo-Infective Modules. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 359-366. doi: 10.4153/CMB-1975-065-3
@article{10_4153_CMB_1975_065_3,
     author = {Jain, S. K. and Singh, Surjeet},
     title = {Quasi-Injective and {Pseudo-Infective} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {359--366},
     year = {1975},
     volume = {18},
     number = {3},
     doi = {10.4153/CMB-1975-065-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-065-3/}
}
TY  - JOUR
AU  - Jain, S. K.
AU  - Singh, Surjeet
TI  - Quasi-Injective and Pseudo-Infective Modules
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 359
EP  - 366
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-065-3/
DO  - 10.4153/CMB-1975-065-3
ID  - 10_4153_CMB_1975_065_3
ER  - 
%0 Journal Article
%A Jain, S. K.
%A Singh, Surjeet
%T Quasi-Injective and Pseudo-Infective Modules
%J Canadian mathematical bulletin
%D 1975
%P 359-366
%V 18
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-065-3/
%R 10.4153/CMB-1975-065-3
%F 10_4153_CMB_1975_065_3

[1] 1. Eisenbud, D. and Griffith, P., Serial rings, J. Algebra 17 (1971), 389-400. Google Scholar

[2] 2. Eisenbud, D. and Robson, J. C., Hereditary noetherian prime rings, J. Algebra 16 (1970), 86-104. Google Scholar

[3] 3. Faith, C., Lectures on injective modules and quotient rings, Lecture Notes in Math., No. 49 (1967), Springer-Verlag. Google Scholar

[4] 4. Hallett, R. R., Injective modules and their generalizations, Ph.D. thesis, Univ. of British Columbia, Vancouver, Dec. 1971. Google Scholar

[5] 5. Harada, M., Note on quasi-injective modules, Osaka J. Math. 2 (1965), 351-356. Google Scholar

[6] 6. Johnson, R. E., Quotient rings of rings with zero singular ideal, Pacific J. Math. 11 (1961), 1385-1392. Google Scholar

[7] 7. Johnson, R. E. and Wong, E. T., Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260-268. Google Scholar

[8] 8. Lenagan, T. H., Bounded hereditary noetherian prime rings, J. London Math. Soc. 6 (1973), 241-246. Google Scholar

[9] 9. Levy, L., Torsion free and divisible modules over non-integral domains, Canadian J. Math. 15 (1963), 132-151. Google Scholar

[10] 10. Matlis, E., Injective modules over noetherian rings, Pacific J. Math. 8 (1958), 511-528. Google Scholar

[11] 11. McConnell, J. C. and Robson, J. C., Homomorphisms and extensions of modules over certain differential polynomial rings, J. Algebra 26 (1973), 319-342. Google Scholar

[12] 12. Nakayama, T., On Frobeniusean algebras II, Ann. Math. (2) 42 (1941), 1-21. Google Scholar

[13] 13. Singh, S. and Jain, S. K., On pseudo-injective modules and self pseudo-injective rings, J. Math. Sci. 2(1967), 23-31. Google Scholar

[14] 14. Singh, S., On pseudo-injective modules, Rivisto. Mat. Univ. Parma, 9 (1968), 59-65. Google Scholar

[15] 15. Singh, S. and Wason, K., Pseudo-injective modules over commutative rings, J. Indian Math. Soc. 34 (1970), 61-66. Google Scholar

[16] 16. Singh, S., Quasi-injective and quasi-projective modules over hereditary noetherian prime rings, Canadian J. Math, (to appear). Google Scholar

[17] 17. Teply, M. L., Private communication. Google Scholar

[18] 18. Teply, M. L., Pseudo-injective modules which are not quasi-injective, Proc. Amer. Math. Soc. (to appear). Google Scholar

Cité par Sources :