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On Some Properties of Hollow and Hollow Dimension Modules

Received: 18 August 2013     Published: 30 September 2013
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Abstract

No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 5)
DOI 10.11648/j.pamj.20130205.12
Page(s) 156-161
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Hollow Module, Indecomposable Module, Hollow Dimension Module, Hollow-Lifting Module

References
[1] A. Idelhadj, R. Tribak, On Some Properties of ⊕-Supplemented Modules, IJMMS :69, 4373–4387, 2003.
[2] C. Lomp, On Dual Goldie Dimension, Diplomarbeit (M. Sc. Thesis), Doesseldorf (1996).
[3] C. Lomp, On semilocal modules and rings, Comm. Algebra 27(4), (1999), PP. 1921-1935.
[4] D. Keskinl and C. Lomp, On Lifting LE-Modules, Vietnam Journal ol Mathematics 3O:2, 167-176, 2002.
[5] D. Keskin, On lifting modules, Comm. Algebra, 28(7) , 3427-3440, 2000.
[6] D. Herbera and A. Shamsuddin, Moduleswith Semi-local Endomorphism Ring, proceedings of the american mathematical society, Vol 123, No 12, 1995.
[7] D. K. Tutuncu and S. H. Mohamed, Weak Lifting Modules with Small Radical, Ring and Module Theory Trends in Mathematics, 129–134, 2010 Springer Basel AG.
[8] E. Turkmen and A. Pancar, On Radical Supplemented Modules, International Journal of Computational Cognition, Vol. 7, No. 1, MARCH 2009.
[9] J. Clark, C. Lomp, N. Vajana, and R. Wisbauer. Lifting Modules. Birkhauser Verlag Basel, Boston-Berlin, 2006. 22:3
[10] N. Orhan, D. K.Tutuncu and R.Tribak, On Hollow-Lifting Modules,Taiwanese Journal of Mathematics,Vol. 11, No. 2, 545-568, June 2007.
[11] O. Nil, K. T. Derya, Hollow dimension of modules, J Zhejiang Univ SCI 2, 6A(10):1055-1057, 2005.
[12] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading, Philadelphia, (1991).
[13] S. H. Mohamed and B. J. Muller, Continuous and discrete modules, London Math. Soc. LNS 147 Cambridge Univ. Press, Cambridge, 1990., Proposition A.7
[14] S. Top, Totally weak Supplemented Modules, Thesis Master, July (2007), Izmir.
[15] T. Amoozegar, On Generalized Lifting Modules,Tarbiat Moallem University, 20th Seminar on Algebra,2-3 Ordibehesht, 1388 (Apr. 22-23, 2009) pp 21-23.
[16] Y. Talebi, A Generalization of Lifting Modules, Int. J. Contemp. Math. Sciences, Vol. 2, no. 22, 1069 – 1075, 2007.
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  • APA Style

    Majid Mohammed, Abd Ghafur Bin Ahmad. (2013). On Some Properties of Hollow and Hollow Dimension Modules. Pure and Applied Mathematics Journal, 2(5), 156-161. https://doi.org/10.11648/j.pamj.20130205.12

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    ACS Style

    Majid Mohammed; Abd Ghafur Bin Ahmad. On Some Properties of Hollow and Hollow Dimension Modules. Pure Appl. Math. J. 2013, 2(5), 156-161. doi: 10.11648/j.pamj.20130205.12

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    AMA Style

    Majid Mohammed, Abd Ghafur Bin Ahmad. On Some Properties of Hollow and Hollow Dimension Modules. Pure Appl Math J. 2013;2(5):156-161. doi: 10.11648/j.pamj.20130205.12

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  • @article{10.11648/j.pamj.20130205.12,
      author = {Majid Mohammed and Abd Ghafur Bin Ahmad},
      title = {On Some Properties of Hollow and Hollow Dimension Modules},
      journal = {Pure and Applied Mathematics Journal},
      volume = {2},
      number = {5},
      pages = {156-161},
      doi = {10.11648/j.pamj.20130205.12},
      url = {https://doi.org/10.11648/j.pamj.20130205.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130205.12},
      abstract = {No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.},
     year = {2013}
    }
    

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    AB  - No doubt, a notion of the hollow dimension modules can constitute a very important situation in the module theory. Therefore, our work presents a key role mainly in some properties and characterizations of hollow and hollow dimension module. We prove that if R be a V-ring and M is semisimple with indecomposable property, then M is hollow module. Also we study characterization the relation between lifting property and hollow-lifting module. We prove that if M is a nonzero indecomposable and lifting module over a commutative noetherian ring R then M is hollow module. Let M be an R-module and N be a submodule of M if hdim(M) = hdim(M/N) + hdim(N), then M is supplemented module.
    VL  - 2
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    ER  - 

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Author Information
  • School of Mathematical Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia

  • School of Mathematical Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia

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