Quasi-small P-injective Modules

Main Article Content

Sarun Wongwai

Abstract

Let M be a right R-module. A right R-module N is called M-small principally injective (brie y, M-small P-injective) if, every R-homomorphism from anM-cyclic small submodule ofM to N can be extended to an R-homomorphism
from M to N: In this paper we give some characterizations and properties of quasi-small principally injective modules.


2000 Mathematics Subject Classication : 16D50, 16D70, 16D80

Article Details

How to Cite
1.
Wongwai S. Quasi-small P-injective Modules. Prog Appl Sci Tech. [Internet]. 2011 Aug. 23 [cited 2024 Nov. 15];1(1):59-65. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/243267
Section
Mathematics and Applied Statistics

References

F. W. Anderson and K. R. Fuller, Rings and Categories of Modules," Graduate Texts in Math.No.13 ,Springer-verlag, New York, 1992.

V. Camillo, Commutative rings whose principal ideals are annihilators, Portugal Math., 46(1989), 33{37.

A. Haghany and M. R. Vedadi, Modules whose injective endomorphisms are essential, J. Algebra, 243(2001), 765{779.

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, 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 quasi- principally injective modules, Algebra Coll.6: 3(1999), 269{276.

L. Shen and J. Shen Small injective rings, arXiv: Math., RA/0505445 v.1 (2005).

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) pp. 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), pp. 27-33.

S. Wongwai, Small Principally Quasi-injective modules, Int. J. Contemp. Math. Sciences, Vol.6, no. 11, 527-534.