On Some Properties of Hollow and Hollow Dimension Modules

Majid Mohammed; Abd Ghafur Bin Ahmad

doi:doi:10.11648/j.pamj.20130205.12

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On Some Properties of Hollow and Hollow Dimension Modules

Majid Mohammed, Abd Ghafur Bin Ahmad

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 5)

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

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[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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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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TY  - JOUR
T1  - On Some Properties of Hollow and Hollow Dimension Modules
AU  - Majid Mohammed
AU  - Abd Ghafur Bin Ahmad
Y1  - 2013/09/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130205.12
DO  - 10.11648/j.pamj.20130205.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 156
EP  - 161
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130205.12
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
IS  - 5
ER  -

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Author Information

Majid Mohammed

School of Mathematical Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia
Abd Ghafur Bin Ahmad

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - On Some Properties of Hollow and Hollow Dimension Modules
AU  - Majid Mohammed
AU  - Abd Ghafur Bin Ahmad
Y1  - 2013/09/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130205.12
DO  - 10.11648/j.pamj.20130205.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 156
EP  - 161
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130205.12
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
IS  - 5
ER  -

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