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A Note on Localization of Supplemented Modules

Received: 4 March 2014     Accepted: 27 June 2014     Published: 10 July 2014
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Abstract

In this paper we study on commutative rings with identity and all modules are unital left R-modules unless otherwise stated. We define the concept of small submodules for localization modules and additionally, we present the relation between an R-module M and an R_p-localization module M_p for all maximal ideals of R in view of being supplemented.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 3)
DOI 10.11648/j.pamj.20140303.12
Page(s) 66-69
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), 2014. Published by Science Publishing Group

Keywords

Small Submodule, Supplemented Module, Multiplicative Closed Set, Localization Module

References
[1] Alizade, R., Pancar, A., 1991. Homoloji Cebire Giriş, Ondokuz Mayıs Üniversitesi Fen Edebiyat Fakültesi, Samsun.
[2] Anderson, F.W., Fuller K.R., 1974, Rings and Categories of Modules, Springer-Verlag, New York-Heidelberg-Berlin.
[3] Çallıalp, F., Tekir, Ü., 2009. Değişmeli Halkalar ve Modüller, Birsen Yayınevi, İstanbul.
[4] Faith, C., 1976, Algebra II: Ring Theory, Springer- Verlag, Berlin.
[5] Hungerford, T.W., 1973. Algebra, Springer-Verlag, New York.
[6] Lam, T. Y., Lectures on modules and rings, ser. Graduate texts in Mathematics. New York: Springer, 1999, vol. 189.
[7] Larsen, M.D., McCarthy, P.J., 1971. Multiplicative Theory of Ideals, Academic Press, New York and London.
[8] Moore, D.G., 1968. Prime and Radical Submodules of Modules over Commutative Rings, Vol.30, No.10, 5037-5064.
[9] Mohamed, S. H. and Müller, B. J., Continuous and discrete modules, ser. London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 1990, vol. 147.
[10] Sharpe, D.W., Vamos, P., 1972. Injective Modules, Cambridge University Press.
[11] Taşçı, D., 2007. Soyut Cebir, Alp Yayınevi, Ankara.
[12] Northcott, D.G., 1968. Lessons on Rings, Modules and Multiplicity, Cambridge University Press.
[13] J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, 2006. Lifting Modules, Supplements and projectivity in module theory, Front. Math., Birkhauser Verlag, Basel.
[14] Wisbauer, R., 1991. Foundations of Module and Ring Theory, Gordon and Breach (Philadelphia).
[15] Shang, Y. On the ideals of commutative local rings, Kochi Journal of Mathematics, 2013, vol. 8, 13--17.
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  • APA Style

    Esra Öztürk, Şenol Eren. (2014). A Note on Localization of Supplemented Modules. Pure and Applied Mathematics Journal, 3(3), 66-69. https://doi.org/10.11648/j.pamj.20140303.12

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    ACS Style

    Esra Öztürk; Şenol Eren. A Note on Localization of Supplemented Modules. Pure Appl. Math. J. 2014, 3(3), 66-69. doi: 10.11648/j.pamj.20140303.12

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    AMA Style

    Esra Öztürk, Şenol Eren. A Note on Localization of Supplemented Modules. Pure Appl Math J. 2014;3(3):66-69. doi: 10.11648/j.pamj.20140303.12

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  • @article{10.11648/j.pamj.20140303.12,
      author = {Esra Öztürk and Şenol Eren},
      title = {A Note on Localization of Supplemented Modules},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {3},
      pages = {66-69},
      doi = {10.11648/j.pamj.20140303.12},
      url = {https://doi.org/10.11648/j.pamj.20140303.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140303.12},
      abstract = {In this paper we study on commutative rings with identity and all modules are unital left R-modules unless otherwise stated. We define the concept of small submodules for localization modules and additionally, we present the relation between an R-module M and an R_p-localization module M_p for all maximal ideals of R in view of being supplemented.},
     year = {2014}
    }
    

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    AB  - In this paper we study on commutative rings with identity and all modules are unital left R-modules unless otherwise stated. We define the concept of small submodules for localization modules and additionally, we present the relation between an R-module M and an R_p-localization module M_p for all maximal ideals of R in view of being supplemented.
    VL  - 3
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    ER  - 

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