Some characterizations of semiprime Goldie rings
Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 357-365

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

The notation in this paper will be standard and it may be found in [3], for example. In particular, the notation A ⊂′ B stands for the statement “A is an essential submodule of B”. As is customary, we say that a ring R is a Goldie ring when R is both left and right Goldie. Similarly, a ring is noetherian if and only if it is both right and left noetherian, etc.
López-Permouth, S. R.; Rizvi, S. Tariq; Yousif, M. F. Some characterizations of semiprime Goldie rings. Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 357-365. doi: 10.1017/S0017089500009940
@article{10_1017_S0017089500009940,
     author = {L\'opez-Permouth, S. R. and Rizvi, S. Tariq and Yousif, M. F.},
     title = {Some characterizations of semiprime {Goldie} rings},
     journal = {Glasgow mathematical journal},
     pages = {357--365},
     year = {1993},
     volume = {35},
     number = {3},
     doi = {10.1017/S0017089500009940},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009940/}
}
TY  - JOUR
AU  - López-Permouth, S. R.
AU  - Rizvi, S. Tariq
AU  - Yousif, M. F.
TI  - Some characterizations of semiprime Goldie rings
JO  - Glasgow mathematical journal
PY  - 1993
SP  - 357
EP  - 365
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009940/
DO  - 10.1017/S0017089500009940
ID  - 10_1017_S0017089500009940
ER  - 
%0 Journal Article
%A López-Permouth, S. R.
%A Rizvi, S. Tariq
%A Yousif, M. F.
%T Some characterizations of semiprime Goldie rings
%J Glasgow mathematical journal
%D 1993
%P 357-365
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009940/
%R 10.1017/S0017089500009940
%F 10_1017_S0017089500009940

[1] 1.Al-Huzali, A. H., Jain, S. K. and López-Permouth, S. R., Rings whose cyclics have finite Goldie dimension, to appear in J. Algebra. Google Scholar

[2] 2.Al-Huzali, A. H., Jain, S. K. and López-Permouth, S. R., Weakly-injective rings and modules, Osaka J. Math. 29 (1992), 75–87. Google Scholar

[3] 3.Anderson, F. W. and Fuller, K. R., Rings and categories of modules (Springer, 1974). Google Scholar | DOI

[4] 4.Boyle, A. K., Hereditary Ql-rings, Trans. Amer. Math. Soc. 192 (1974), 115–120. Google Scholar

[5] 5.Boyle, A. K., Injectives containing no proper quasi-injective submodules, Comm. Algebra 4 (1976), 775–785. Google Scholar | DOI

[6] 6.Boyle, A. K. and Goodearl, K. R., Rings over which certain modules are injective, Pacific J. Math. 58 (1975), 43–53. Google Scholar | DOI

[7] 7.Camillo, V. P., Modules whose quotients have finite Goldie dimension, Pacific J. Math. 69 (1977), 337–338. Google Scholar | DOI

[8] 8.Chatters, A. W. and Hajarnavis, C. R., Rings with chain conditions (Pitman, 1980). Google Scholar

[9] 9.Cozzens, J. and Faith, C., Simple Noetherian rings (Cambridge University Press, 1975). Google Scholar | DOI

[10] 10.Faith, C., On hereditary rings and Boyle's conjecture, Arch. Math. (Basel) 27 (1976), 113–119. Google Scholar | DOI

[11] 11.Golan, J. S. and López-Permouth, S. R., Ql-filters and tight modules, Comm. Algebra 19 (1991), 2217–2229. Google Scholar | DOI

[12] 12.Jain, S. K., López-Permouth, S. R. and Singh, S., On a class of Ql-rings, Glasgow Math. J. 34 (1992), 75–81. Google Scholar | DOI

[13] 13.Jategaonkar, A. V., Localization in Noetherian rings (Cambridge University Press, 1986). Google Scholar | DOI

[14] 14.Kosler, K. A., On hereditary and Noetherian V-rings, Pacific J. Math. 103 (1982), 467–473. Google Scholar | DOI

[15] 15.Kurshan, R. P., Rings whose cyclic modules have finitely generated socle, J. Algebra 15 (1970), 376–386. Google Scholar | DOI

[16] 16.López-Permouth, S. R., Rings characterized by their weakly-injective modules, Glasgow Math J. 34 (1992), 349–353. Google Scholar | DOI

[17] 17.Page, S. S. and Yousif, M. F., Relative injectivity and chain conditions, Comm. Algebra 17 (1989), 899–924. Google Scholar | DOI

[18] 18.Schock, R. C., Dual generalizations of the Artinian and Noetherian conditions, Pacific J. Math. 54 (1974), 227–235. Google Scholar | DOI

[19] 19.Warfield, R. B., Decompositions of injective modules, Pacific J. Math. 31 (1969), 263–276. Google Scholar | DOI

Cité par Sources :