Title:
|
On generalization of injectivity (English) |
Author:
|
Yue Chi Ming, R. |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
28 |
Issue:
|
2 |
Year:
|
1992 |
Pages:
|
215-220 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Characterizations of quasi-continuous modules and continuous modules are given. A non-trivial generalization of injectivity (distinct from $p$-injectivity) is considered. (English) |
Keyword:
|
continuous modules |
Keyword:
|
quasi-continuous modules |
Keyword:
|
injective modules |
Keyword:
|
quasi-Frobeniusean rings |
Keyword:
|
m-injective rings |
MSC:
|
16D50 |
MSC:
|
16D70 |
MSC:
|
16L60 |
MSC:
|
16W20 |
idZBL:
|
Zbl 0786.16003 |
idMR:
|
MR1222289 |
. |
Date available:
|
2008-06-06T21:22:59Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107453 |
. |
Reference:
|
[1] Camillo, V., Yousif, M. F.: Continuous rings with ACC on annihilators.. |
Reference:
|
[2] Faith, C.: Algebra II:Ring Theory.Grundlehren 191 (1976), Springer Verlag. MR 0427349 |
Reference:
|
[3] Hirano, Y., Tominaga, H.: Regular rings , $V$-rings and their generalizations.Hiroshima Math J. 9 (1979), 137-149. MR 0529329 |
Reference:
|
[4] Jain, S. K., Loper-Permouth and Rizvi, T.: Continuous rings with ACC on essential are Artinian.Proc. Amer. Math. Soc. |
Reference:
|
[5] Michler, G. O., Villamaryor, O. E.: On rings whose simple modules are injective.J. Algebra 25 (1973), 185-201. MR 0316505 |
Reference:
|
[6] Mohamed, S. H., Muller, B. J.: Continuous and discrete modules.London Math. Soc. Lecture note Series 147 (Cambridge University Press) (1990). MR 1084376 |
Reference:
|
[7] Ohori, M.: Chain conditions and quotient rings of pp. rings.Math. J. Okayama Univ. 30 (1988), 71-78. MR 0976734 |
Reference:
|
[8] Storrer, H. H.: A note on quasi–Frobenius rings and ring epimorphisms.Canad. Math. Bull. 12 (1969), 287-292. Zbl 0182.36704, MR 0251075 |
Reference:
|
[9] Takehana, Y.: $V$-rings relative to hereditary torsion theories.Tsukuba J. Math. 6 (1982), 293-298. Zbl 0529.16009, MR 0705120 |
Reference:
|
[10] Utumi, Y.: On continuous rings and self-injective rings.Trans. Amer. Math. Soc. 118 (1965), 158-173. Zbl 0144.27301, MR 0174592 |
Reference:
|
[11] Varadarajan, K.: Generalised $V$-rings and torsion theories.Comm. Algebra 14 (1986), 455-467. MR 0823346 |
Reference:
|
[12] Varadarajan, K., Wehrhan K.: $P$-injectivity of simple pretorsion modules.Glasgow Math. J. 28 (1986), 223-225. MR 0848429 |
Reference:
|
[13] Xue, Weimin: On p.p.rings.Kobe Math. 7 (1990), 77-80. MR 1077571 |
Reference:
|
[14] Yousif, M. F.: $SI$-modules.Math. J. Okayama Univ. 28 (1986), 133-146. Zbl 0621.16027, MR 0885022 |
Reference:
|
[15] Yue Chi Ming, R.: On $V$-rings and prime rings.J. Algebra 62 (1980), 13-20. Zbl 0429.16018, MR 0561114 |
Reference:
|
[16] Yue Chi Ming, R.: On von Neumann regular rings.XIII. Ann. Univ. Ferrara Sez. VII, Sc. Mat. 31 (1985), 49-61. Zbl 0602.16012, MR 0841852 |
Reference:
|
[17] Yue Chi Ming, R.: On injectivity and $p$-injectivity.J. Math. Kyoto Univ. 27 (1987), 439-452. Zbl 0655.16012, MR 0910229 |
Reference:
|
[18] Yue Chi Ming, R.: On von Neumann regular rings.XV. Acta Math. Vietnamica 13 (1988), 71-79. Zbl 0685.16009, MR 1023706 |
Reference:
|
[19] Yue Chi Ming, R.: A note on regular rings.Bull. Soc. Math. Belgique Ser. B 41 (1989), 129-138. Zbl 0672.16011, MR 1044007 |
. |