Small PPQ-injective Modules
Main Article Content
Abstract
Let M be a right R −module. A right R −module N is called small pseudo principally M−injective (briefly, small PP −M− injective) if, every R −monomorphism from a small and principal submodule of M to Ncan be extended to an R − homomorphism from M toN . In this paper, we give some characterizations and properties of small PP −Q− injective modules.
2010 Mathematics Subject Classification: 13C10, 13C11, 13C60.
Article Details
References
F. W. Anderson and K. R. Fuller, “Rings and Categories of Modules”, Graduate Texts in Math. No.13 ,Springer-verlag, New York, 1992.
N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, “Extending Modules”, Pitman, London, 1994.
A. Facchini, “Module Theory”, Birkhauser Verlag, Basel, Boston, Berlin,1998.
S. H. Mohamed and B. J. Muller, “Continuous and Discrete Modules”, London Math. Soc. Lecture Note Series 14, Cambridge Univ. Press, 1990.
W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174(1995), 77 - 93.
W. K. Nicholson and M. F. Yousif, Mininjective rings, J. Algebra, 187(1997), 548 - 578.
W. K. Nicholson, J. K. Park and M. F. Yousif, Principally quasi-injective modules, Comm. Algebra, 27:4(1999), 1683 - 1693.
N. V. Sanh, K. P. Shum, S. Dhompongsa and S. Wongwai, On quasiprincipally injective modules, Algebra Coll.6: 3(1999), 269 - 276.
L.V. Thuyet, and T.C.Quynh, On small injective rings, simple-injective and quasi-Frobenius rings, Acta Math. Univ. Comenianae, Vol.78(2), (2009), 161 - 172.
R. Wisbauer, “Foundations of Module and Ring Theory”, Gordon and Breach London, Tokyo e.a., 1991.
S. Wongwai, On the endomorphism ring of a semi-injective module, Acta Math. Univ. Comenianae, Vol.71, 1(2002), 27 - 33.
S. Wongwai, Small Principally Quasi-injective modules, Int. J. Contemp. Math. Sciences, Vol.6, No. 11, 527 - 534.
Z. Zhu, Pseudo PQ-injective modules, Trk J Math, 34(2010), 1- 8.