S-Injective Modules and Rings

DOI: 10.4236/apm.2014.41004   PDF   HTML   XML   3,323 Downloads   5,565 Views   Citations


We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their modules.

Share and Cite:

N. Zeyada, "S-Injective Modules and Rings," Advances in Pure Mathematics, Vol. 4 No. 1, 2014, pp. 25-33. doi: 10.4236/apm.2014.41004.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] C. Faith, “Algebra II Ring Theory,” Springer-Verlag, Berlin, 1976.
[2] F. Kasch, “Modules and Rings,” L.M.S. Monograph No. 17. Academic Press, New York, 1982.
[3] W. K. Nicholson and M. F. Yousif, “Quasi-Frobenius Rings,” In: Cambridge Tracts in Mathematics, Vol. 158, Cambridge University Press, Cambridge, 2003. http://dx.doi.org/10.1017/CBO9780511546525
[4] M. F. Yousif and Y. Zhou, “Semi-Regular, Semi-Perfect and Perfect Rings Relative to an Ideal,” Rocky Mountain Journal of Mathematics, Vol. 32, No. 4, 2002, pp. 1651-1671. http://dx.doi.org/10.1216/rmjm/1181070046
[5] K. R. Goodearl, “Singular Torsion and the Splitting Properties,” Memoirs of the American Mathematical Society, Vol. 124, 1972.
[6] F. W. Anderson and K. R. Fuller, “Rings and Categories of Modules,” Springer-Verlag, Berlin/New York, 1974.
[7] M. F. Yousif, Y. Zhou and N. Zeyada, “On Pseudo-Frobenius rings,” Canadian Mathematical Bulletin, Vol. 48, No. 2, 2005, pp. 317-320. http://dx.doi.org/10.4153/CMB-2005-029-5

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.