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A Generalized Version of 𝒆-Supplemented Modules Relative to a Torsion Theory

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 76 - 82, 28.02.2020

Esra Sözen

https://doi.org/10.18185/erzifbed.619098
Cited By: 1

Abstract

The objective of this aim to obtain a torsion theoretic analogue of e-supplemented modules. For this, firstly we define 𝜏𝑒-submodule of a module and give basic properties of this concept. After that, 𝜏𝑒-supplemented modules and 𝜏𝑒-hollow modules are introduced and investigated some fundamental properties of these modules.

Keywords

Hereditary torsion theory 𝜏𝑒-small submodule 𝜏𝑒-supplemented module 𝜏𝑒-hollow module.

References

  • Bland, P. E. 1998. ‘Topics in Torsion Theory’, Mathematical Research, 103, Wiley-VCH, Berlin.
  • Charalambides, S. and Clark, J. 2007. ‘CS Modules Relative to a Torsion Theory, Mediterr. J. Math., 4, 291-308.
  • Clark, J., Lomp, C., Vanaja, N., and Wisbauer, R. (2006). Lifting modules: Supplements and Projectivity in Module Theory, Birkhauser, Verlag, Basel.
  • Koşan M.T., 2007. δ-lifting and δ-supplemented modules, Algebra Colloq., 14(1), 53 - 60.
  • Koşar, B., Nebiyev, C. and Sökmez, N. (2015). ‘G-supplemented Modules’, Ukrainian Mathematical Journal, 67(6): 861-864.
  • Quynh, T. C. and Tin, P. H. 2013. ‘Some Properties of e-supplemented and e-lifting modules’, Vietnam Journal of Mathematics, 41(3), 303-312.
  • Zhou, Y., 2000. Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq., 7(3), 305-318.
  • Zhou, D. X. and Zhang, X. R. 2011. ‘Small-Essential Submodules and Morita Duality’ Southeast Asian bulletin of Mathematics, 35(6), 1051-1062.

e-Tümlenmiş Modüllerin Torsiyon Teorisine Göre Genelleştirilmiş bir Versiyonu

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 76 - 82, 28.02.2020

Esra Sözen

https://doi.org/10.18185/erzifbed.619098
Cited By: 1

Abstract

Bu çalışmanın amacı e-tümlenmiş modüllerin
torsiyon-teorik bir genelleştirmesini elde etmektir. Bunun için öncelikle bir modülün Te -küçük alt modülleri
tanımlanarak temel özelliklerine değinildi. Ardından Te -tümlenmiş modül ve Te -oyuk modül kavramlarına
yer verilerek bunlara ilişkin temel teorik özellikler irdelendi.

Keywords

Kalıtsal torsiyon teorisi τ_e-küçük alt modül 𝜏𝑒-tümlenmiş modül 𝜏𝑒-oyuk modül

References

  • Bland, P. E. 1998. ‘Topics in Torsion Theory’, Mathematical Research, 103, Wiley-VCH, Berlin.
  • Charalambides, S. and Clark, J. 2007. ‘CS Modules Relative to a Torsion Theory, Mediterr. J. Math., 4, 291-308.
  • Clark, J., Lomp, C., Vanaja, N., and Wisbauer, R. (2006). Lifting modules: Supplements and Projectivity in Module Theory, Birkhauser, Verlag, Basel.
  • Koşan M.T., 2007. δ-lifting and δ-supplemented modules, Algebra Colloq., 14(1), 53 - 60.
  • Koşar, B., Nebiyev, C. and Sökmez, N. (2015). ‘G-supplemented Modules’, Ukrainian Mathematical Journal, 67(6): 861-864.
  • Quynh, T. C. and Tin, P. H. 2013. ‘Some Properties of e-supplemented and e-lifting modules’, Vietnam Journal of Mathematics, 41(3), 303-312.
  • Zhou, Y., 2000. Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq., 7(3), 305-318.
  • Zhou, D. X. and Zhang, X. R. 2011. ‘Small-Essential Submodules and Morita Duality’ Southeast Asian bulletin of Mathematics, 35(6), 1051-1062.
There are 8 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Esra Sözen 0000-0002-2632-2193

Publication Date February 28, 2020
Published in Issue Year 2020 Volume: 13 Issue: ÖZEL SAYI I

Cite

APA Sözen, E. (2020). e-Tümlenmiş Modüllerin Torsiyon Teorisine Göre Genelleştirilmiş bir Versiyonu. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 76-82. https://doi.org/10.18185/erzifbed.619098

Cited By

Bol E-Tümlenmiş Modüllere ve E-Yükseltilebilir Modüllere Torsiyon-Teorik Bir Yaklaşım
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Esra SÖZEN
https://doi.org/10.18185/erzifbed.690071