| Title:
|
Some results on quasi-Frobenius rings (English) |
| Author:
|
Zhu, Zhanmin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
147-151 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give some new characterizations of quasi-Frobenius rings by the generalized injectivity of rings. Some characterizations give affirmative answers to some open questions about quasi-Frobenius rings; and some characterizations improve some results on quasi-Frobenius rings. (English) |
| Keyword:
|
mininjective ring |
| Keyword:
|
YJ-injective ring |
| Keyword:
|
$2$-injective ring |
| Keyword:
|
JGP-injective ring |
| Keyword:
|
quasi-Frobenius ring |
| MSC:
|
16D50 |
| MSC:
|
16L30 |
| MSC:
|
16L60 |
| MSC:
|
16P60 |
| MSC:
|
16P70 |
| idZBL:
|
Zbl 06773710 |
| idMR:
|
MR3666937 |
| DOI:
|
10.14712/1213-7243.2015.202 |
| . |
| Date available:
|
2017-06-13T13:21:51Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146784 |
| . |
| Reference:
|
[1] Björk J.E.: Rings satisfying certain chain conditions.J. Reine Angew. Math. 245 (1970), 63–73. Zbl 0211.36401, MR 0277562 |
| Reference:
|
[2] Camillo V., Yousif M.F.: Continuous rings with ACC on annihilators.Canad. Math. Bull. 34 (1991), no. 4, 462–464. Zbl 0767.16004, MR 1136646, 10.4153/CMB-1991-074-x |
| Reference:
|
[3] Chen J.L., Zhou Y.Q., Zhu Z.M.: GP-injective rings need not be P-injective.Comm. Algebra 33 (2005), no. 7, 2395–2402. Zbl 1076.16003, MR 2153231, 10.1081/AGB-200058375 |
| Reference:
|
[4] Nam S.B., Kim N.K., Kim J.Y.: On simple GP-injective modules.Comm. Algebra 23 (1995), no. 14, 5437–5444. Zbl 0840.16006, MR 1363614, 10.1080/00927879508825543 |
| Reference:
|
[5] Nicholson W.K., Yousif M.F.: Principally injective rings.J. Algebra 174 (1995), no. 1, 77–93. Zbl 0839.16004, MR 1332860, 10.1006/jabr.1995.1117 |
| Reference:
|
[6] Nicholson W.K., Yousif M.F.: Mininjective rings.J. Algebra 187 (1997), no. 2, 548–578. Zbl 0879.16002, MR 1430998, 10.1006/jabr.1996.6796 |
| Reference:
|
[7] Nicholson W.K., Yousif M.F.: Quasi-Frobenius Rings.Cambridge University Press, Cambridge, 2003. Zbl 1042.16009, MR 2003785 |
| Reference:
|
[8] Rutter E.A.: Rings with the principle extension property.Comm. Algebra 3 (1975), no. 3, 203–212. MR 0382337, 10.1080/00927877508822043 |
| Reference:
|
[9] Yousif M.F., Zhou Y.Q.: Rings for which certain elements have the principal extension property.Algebra Colloq. 10 (2003), no. 4, 501–512. Zbl 1040.16004, MR 2013743 |
| Reference:
|
[10] Yue Chi Ming R.: On regular rings and self-injective rings II.Glasnik Mat. 18 (1983), no. 2, 221–229. Zbl 0528.16006, MR 0733161 |
| Reference:
|
[11] Yue Chi Ming R.: On quasi-Frobeniusean and Artinian rings.Publ. Inst. Math. (Beograd) (N.S.) 33 (1983), no. 47, 239–245. Zbl 0521.16009, MR 0723453 |
| Reference:
|
[12] Yue Chi Ming R.: On regular rings and artinian rings II.Riv. Math. Univ. Parma 11 (1985), no. 4, 101–109. Zbl 0611.16011, MR 0851520 |
| Reference:
|
[13] Yue Chi Ming R.: On p-injectivity, YJ-injectivity and quasi-Frobenius rings.Comment. Math. Univ. Carolin. 43 (2002), no. 1, 33–42. MR 1903305 |
| Reference:
|
[14] Yue Chi Ming R.: On YJ-injectivity and annihilators.Georgian Math. J. 12 (2005), no. 3, 573–581. Zbl 1090.16002, MR 2174959 |
| Reference:
|
[15] Zhou Y.Q.: Rings in which certain right ideal are direct summands of annihilators.J. Aust. Math. Soc. 73 (2002), no. 3, 335–346. MR 1936257, 10.1017/S1446788700009009 |
| Reference:
|
[16] Zhu Z.M.: Almost MGP-injective rings.Ukrainian Math. J. 65 (2014), no. 11, 1634–1641. Zbl 1311.16001, MR 3216859, 10.1007/s11253-014-0885-z |
| . |
