Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
continuous modules; quasi-continuous modules; injective modules; quasi-Frobeniusean rings; m-injective rings
continuous modules; quasi-continuous modules; injective modules; quasi-Frobeniusean rings; m-injective rings
Summary:
Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from $p$-injectivity) is considered.
References:
[1] Camillo, V., Yousif, M. F.: Continuous rings with ACC on annihilators.
[2] Faith, C.: Algebra II:Ring Theory. Grundlehren 191 (1976), Springer Verlag. MR 0427349
[3] Hirano, Y., Tominaga, H.: Regular rings , $V$-rings and their generalizations. Hiroshima Math J. 9 (1979), 137-149. MR 0529329
[4] Jain, S. K., Loper-Permouth and Rizvi, T.: Continuous rings with ACC on essential are Artinian. Proc. Amer. Math. Soc.
[5] Michler, G. O., Villamaryor, O. E.: On rings whose simple modules are injective. J. Algebra 25 (1973), 185-201. MR 0316505
[6] Mohamed, S. H., Muller, B. J.: Continuous and discrete modules. London Math. Soc. Lecture note Series 147 (Cambridge University Press) (1990). MR 1084376
[7] Ohori, M.: Chain conditions and quotient rings of pp. rings. Math. J. Okayama Univ. 30 (1988), 71-78. MR 0976734
[8] Storrer, H. H.: A note on quasi–Frobenius rings and ring epimorphisms. Canad. Math. Bull. 12 (1969), 287-292. MR 0251075 | Zbl 0182.36704
[9] Takehana, Y.: $V$-rings relative to hereditary torsion theories. Tsukuba J. Math. 6 (1982), 293-298. MR 0705120 | Zbl 0529.16009
[10] Utumi, Y.: On continuous rings and self-injective rings. Trans. Amer. Math. Soc. 118 (1965), 158-173. MR 0174592 | Zbl 0144.27301
[11] Varadarajan, K.: Generalised $V$-rings and torsion theories. Comm. Algebra 14 (1986), 455-467. MR 0823346
[12] Varadarajan, K., Wehrhan K.: $P$-injectivity of simple pretorsion modules. Glasgow Math. J. 28 (1986), 223-225. MR 0848429
[13] Xue, Weimin: On p.p.rings. Kobe Math. 7 (1990), 77-80. MR 1077571
[14] Yousif, M. F.: $SI$-modules. Math. J. Okayama Univ. 28 (1986), 133-146. MR 0885022 | Zbl 0621.16027
[15] Yue Chi Ming, R.: On $V$-rings and prime rings. J. Algebra 62 (1980), 13-20. MR 0561114 | Zbl 0429.16018
[16] Yue Chi Ming, R.: On von Neumann regular rings. XIII. Ann. Univ. Ferrara Sez. VII, Sc. Mat. 31 (1985), 49-61. MR 0841852 | Zbl 0602.16012
[17] Yue Chi Ming, R.: On injectivity and $p$-injectivity. J. Math. Kyoto Univ. 27 (1987), 439-452. MR 0910229 | Zbl 0655.16012
[18] Yue Chi Ming, R.: On von Neumann regular rings. XV. Acta Math. Vietnamica 13 (1988), 71-79. MR 1023706 | Zbl 0685.16009
[19] Yue Chi Ming, R.: A note on regular rings. Bull. Soc. Math. Belgique Ser. B 41 (1989), 129-138. MR 1044007 | Zbl 0672.16011
Search
Partner of
