Article
MSC:
16D50,
16L30,
16L60,
16P60,
16P70 | MR 3666937 | Zbl 06773710 | DOI: 10.14712/1213-7243.2015.202
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
mininjective ring; YJ-injective ring; $2$-injective ring; JGP-injective ring; quasi-Frobenius ring
mininjective ring; YJ-injective ring; $2$-injective ring; JGP-injective ring; quasi-Frobenius ring
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.
References:
[1] Björk J.E.: Rings satisfying certain chain conditions. J. Reine Angew. Math. 245 (1970), 63–73. MR 0277562 | Zbl 0211.36401
[2] Camillo V., Yousif M.F.: Continuous rings with ACC on annihilators. Canad. Math. Bull. 34 (1991), no. 4, 462–464. DOI 10.4153/CMB-1991-074-x | MR 1136646 | Zbl 0767.16004
[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. DOI 10.1081/AGB-200058375 | MR 2153231 | Zbl 1076.16003
[4] Nam S.B., Kim N.K., Kim J.Y.: On simple GP-injective modules. Comm. Algebra 23 (1995), no. 14, 5437–5444. DOI 10.1080/00927879508825543 | MR 1363614 | Zbl 0840.16006
[5] Nicholson W.K., Yousif M.F.: Principally injective rings. J. Algebra 174 (1995), no. 1, 77–93. DOI 10.1006/jabr.1995.1117 | MR 1332860 | Zbl 0839.16004
[6] Nicholson W.K., Yousif M.F.: Mininjective rings. J. Algebra 187 (1997), no. 2, 548–578. DOI 10.1006/jabr.1996.6796 | MR 1430998 | Zbl 0879.16002
[7] Nicholson W.K., Yousif M.F.: Quasi-Frobenius Rings. Cambridge University Press, Cambridge, 2003. MR 2003785 | Zbl 1042.16009
[8] Rutter E.A.: Rings with the principle extension property. Comm. Algebra 3 (1975), no. 3, 203–212. DOI 10.1080/00927877508822043 | MR 0382337
[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. MR 2013743 | Zbl 1040.16004
[10] Yue Chi Ming R.: On regular rings and self-injective rings II. Glasnik Mat. 18 (1983), no. 2, 221–229. MR 0733161 | Zbl 0528.16006
[11] Yue Chi Ming R.: On quasi-Frobeniusean and Artinian rings. Publ. Inst. Math. (Beograd) (N.S.) 33 (1983), no. 47, 239–245. MR 0723453 | Zbl 0521.16009
[12] Yue Chi Ming R.: On regular rings and artinian rings II. Riv. Math. Univ. Parma 11 (1985), no. 4, 101–109. MR 0851520 | Zbl 0611.16011
[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
[14] Yue Chi Ming R.: On YJ-injectivity and annihilators. Georgian Math. J. 12 (2005), no. 3, 573–581. MR 2174959 | Zbl 1090.16002
[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. DOI 10.1017/S1446788700009009 | MR 1936257
[16] Zhu Z.M.: Almost MGP-injective rings. Ukrainian Math. J. 65 (2014), no. 11, 1634–1641. DOI 10.1007/s11253-014-0885-z | MR 3216859 | Zbl 1311.16001
Search
Partner of
