MC2 RINGS AND WQD RINGS*
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 691-702

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

We introduce in this paper the concepts of rings characterized by minimal one-sided ideals and concern ourselves with rings containing an injective maximal left ideal. Some known results for idempotent reflexive rings and left HI rings can be extended to left MC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with non-zero socle and extend some known results for strongly regular rings.
DOI : 10.1017/S0017089509990103
Mots-clés : 16A30, 16A50, 16E50, 16D30
WEI, JUNCHAO; LI, LIBIN. MC2 RINGS AND WQD RINGS*. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 691-702. doi: 10.1017/S0017089509990103
@article{10_1017_S0017089509990103,
     author = {WEI, JUNCHAO and LI, LIBIN},
     title = {MC2 {RINGS} {AND} {WQD} {RINGS*}},
     journal = {Glasgow mathematical journal},
     pages = {691--702},
     year = {2009},
     volume = {51},
     number = {3},
     doi = {10.1017/S0017089509990103},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990103/}
}
TY  - JOUR
AU  - WEI, JUNCHAO
AU  - LI, LIBIN
TI  - MC2 RINGS AND WQD RINGS*
JO  - Glasgow mathematical journal
PY  - 2009
SP  - 691
EP  - 702
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990103/
DO  - 10.1017/S0017089509990103
ID  - 10_1017_S0017089509990103
ER  - 
%0 Journal Article
%A WEI, JUNCHAO
%A LI, LIBIN
%T MC2 RINGS AND WQD RINGS*
%J Glasgow mathematical journal
%D 2009
%P 691-702
%V 51
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990103/
%R 10.1017/S0017089509990103
%F 10_1017_S0017089509990103

[1] 1.Chen, W. X., On semiabelian π-regular rings, Intern. J. Math. Sci. 23 (2007), 1–10. Google Scholar | DOI

[2] 2.Kaplansky, I., Rings of operators (W. A. Benjamin, New York, 1968). Google Scholar

[3] 3.Kim, J. Y., Certain rings whose simple singular modules are GP-injective, Proc. Japan. Acad. 81 (2005), 125–128. Google Scholar

[4] 4.Kim, J. Y. and Baik, J. U., On idempotent reflexive rings, Kyungpook Math. J. 46 (2006), 597–601. Google Scholar

[5] 5.Kim, N. K., Nam, S. B. and Kim, J. Y., On simple singular GP–injective modules, Comm. Algebra 27 (5) (1999), 2087–2096. Google Scholar | DOI

[6] 6.Lam, T. Y. and Dugas, A. S., Quasi-duo rings and stable range descent, J. Pure Appl. Algebra 195 (2005), 243–259. Google Scholar | DOI

[7] 7.Mason, G., Reflexive ideals, Comm. Algebra 9 (17) (1981), 1709–1724. Google Scholar | DOI

[8] 8.Ming, R. Y. C., On regular rings and self-injective rings, ∏, Glasnik Mat. 18 (38) (1983), 25–32. Google Scholar

[9] 9.Nicholson, W. K. and Watters, J. F., Rings with projective socle, Proc. Amer. Math. Soc. 102 (1988), 443–450. Google Scholar | DOI

[10] 10.Nicholson, W. K. and Yousif, M. F., Principally injective rings, J. Algebra 174 (1995), 77–93. Google Scholar | DOI

[11] 11.Nicholson, W. K. and Yousif, M. F., Minijective rings, J. Algebra 187 (1997), 548–578. Google Scholar | DOI

[12] 12.Nicholson, W. K. and Yousif, M. F., Weakly continuous and C2-rings, Comm. Algebra 29 (6) (2001), 2429–2466. Google Scholar | DOI

[13] 13.Osofsky, B. L., Rings all of whose finitely generated modules are injective, Pacific J. Math. 14 (1964), 645–650. Google Scholar | DOI

[14] 14.Rege, M. B., On von Neumann regular rings and SF rings, Math Japonica 31 (1986), 927–936. Google Scholar

[15] 15.Song, X. M. and Yin, X. B., Generalizations of V-rings, Kyungpook Math. J. 45 (2005), 357–362. Google Scholar

[16] 16.Wei, J. C., The rings characterized by minimal left ideal, Acta. Math. Sinica. Engl. Ser. 21 (3) (2005), 473–482. Google Scholar | DOI

[17] 17.Wei, J. C., On simple singular YJ-injective modules, Southeast Asian Bull. Math. 31 (2007), 1009–1018. Google Scholar

[18] 18.Wei, J. C. and Chen, J. H., nil-injective rings, Int. Electron. J. Algebra 2 (2007), 1–21. Google Scholar

[19] 19.Yousif, M. F., On continuous rings, J. Algebra 191 (1997), 495–509. Google Scholar | DOI

[20] 20.Yu, H. P., On quasi-duo rings, Glasgow Math. J. 37 (1995), 21–31. Google Scholar | DOI

[21] 21.Zhang, J. L. and Du, X. N., Hereditary rings containing an injective maximal left ideal, Comm. Algebra 21 (1993), 4473–4479. Google Scholar

Cité par Sources :