Almost Lifiting Modules

Inaam Mohammed Ali Hadi; Ghaleb Ahmed Hammood

doi:https://doi.org/10.14445/22315373/IJMTT-V35P525

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 35 | Number 3 | Year 2016 | Article Id. IJMTT-V35P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P525

Almost Lifiting Modules

Inaam Mohammed Ali Hadi, Ghaleb Ahmed Hammood

Abstract

Let R be a commutative ring with identity and M be an R-module. In this paper we introduce almost lifiting module as a generalization of lifiting modules. The module M is called almost lifiting R-module if for every submodule N of M, there exist submodules A and B such that annM ( annR (N) ) = AB with A  N and B⋂N ˂˂ M. Many results about these concepts are introduced and some relationships between these modules and other related modules are studied.

Keywords

almost lifiting modules, lifiting modules, comultiplication modules.

References

[1] M.S.Abbas, On Fully Stable Modules, Ph.D. Thesis, University of Baghdad, 1991.
[2] Ansari-Toroghy, H. and Farshadifar, F., The dual notion of multiplication modules, J. Math. 11 No. 4, (2007), 1189-1201.
[3] G.Desale and W.K.Nicholson, Endoprimitive Rings, J.Algebra, 70 (1981), 541-560.
[4] N. V. Dungh, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Math Serie, longman, Harlow, 2008.
[5] Z.A.El-Bast and P.F.Smith, Multiplication Modules, Comm.Algebra, 16(1988), 755-774.
[6] P. Fluery, Hollow modules and local endomorphism rings, Pacific J. Math. 53, (1974), 379–385
[7] Ghaleb Ahmed, Strongly hollow submodules and its spectrum, M.Sc. Thesis, College of Education for Pure Science∕ Ibn-Al-Haitham, University of Baghdad, 2012.
[8] Hatem Y. Khalaf, Semimaximal Submodules, Ph.D Thesis, College of Education for Pure Science Ibn-Al-Haitham, Univsity of Baghdad, 2007.
[9] F. Kasch, Modules and Rings, Acad.Press, London, 1982.
[10] A.S.Mijbass, Quasi-Dedekind Modules, Ph.D. Thesis, University of Baghdad, 1997.
[11] S.H.Mohamed and B.J.Muller, Continuous and Discrete Modules, Math.Soc.LNS.147, Cambridge University, 1990.
[12] C.Ozcan, A. Harmanci and P. F. Smith, Duo Modules, Glasgow Math. Journal Trust, 48 (2006) 533–545.

Citation :

Inaam Mohammed Ali Hadi, Ghaleb Ahmed Hammood, "Almost Lifiting Modules," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 3, pp. 177-186, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P525