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Her $\delta-$ Eşatomik Genişlemede $\delta-$ Tümleyene Sahip Modüller

Year 2019, , 47 - 53, 27.06.2019
https://doi.org/10.33484/sinopfbd.503751

Abstract

Bu çalışmada,
Zöschinger’ in
 ve  özelliklerinden uyarlanan  ve  özelliklerine sahip modüller çalışılmıştır.
Eğer
 her  eşatomik
genişlemesinde (yani
 eşatomik) bir tümleyene (sırasıyla
bol
tümleyene) sahip ise  modülüne modül (sırasıyla modül) denir. modülün her direkt
toplam teriminin
modül olduğu ve modülün her alt
modülünün de
modül olduğu
ispatlanmıştır. Eğer
 sol mükemmel halka ise,
her sol
modülün modül olduğu gösterilmiştir.
Ayrıca sol kalıtsal halka üzerindeki
eşatomik,modülün bölüm
modülünün de
modül olduğu
ispatlanmıştır
.

References

  • Clark J, Lomp C, Vanaja N, Wisbauer R, 2006. Lifting Modules, First Edition, Basel: Birkhauser Verlag, 394p.
  • Çalışıcı H, Türkmen E, 2012. Modules that have a supplement in every cofinite extension, Georgian Math. J., 19, 209-216.
  • Kasch F, 1982. Modules and Rings, Second Edition, London New York, 384p.
  • Koşan MT, Harmancı A, 2005. Generalizations of coatomic modules, Cent. Eur. J. Math. 3(2), 273–281.
  • Koşan MT, 2007. lifting and supplemented modules, Algebra Colloq., 14(1), 53 - 60.
  • Özdemir S, 2013. Rad-supplementing modules, J. Korean Math. soc., 53(2), 403-408.
  • Sözen EÖ, Eren Ş, 2017. Modules that have a supplement in every extension, Eur. J. Pure App. Math.,10(4), 70-738.
  • Sözen EÖ, Eryılmaz F, Eren Ş, 2017. Modules that have a weak supplement in every torsion extension, Journal of Science and Arts, 39(2), 269-274.
  • Türkmen BN, 2015. Modules that have a supplement in every coatomic extension, Miskolc Math. Notes, 16(1), 543-551.
  • Tribak R, 2012. Finitely generated supplemented modules are amply supplemented , Bull. Aust. Math. Soc., 86(3), 430-439.
  • Ungör B, Halıcıoğlu S, Harmancı A, 2014. On a class of supplemented modules, Bull. Malays. Math. Sci. Soc., 37(3), 703-717.
  • Wang Y, 2007. small submodules and supplemented modules, Int. J. Math. Math. Sci., Article ID 58132, 8 p.
  • Wisbauer, R, 1991. Foundations of Modules and Rings, Gordon and Breach Science Publishers, Dusseldorff, 616p.
  • Zhou Y, 2000. Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq., 7(3), 305-318.
  • Zöschinger H, 1974. Moduln die in jeder Erweiterung ein Komplement haben, Math. Scand. 35, 267-287.
Year 2019, , 47 - 53, 27.06.2019
https://doi.org/10.33484/sinopfbd.503751

Abstract

References

  • Clark J, Lomp C, Vanaja N, Wisbauer R, 2006. Lifting Modules, First Edition, Basel: Birkhauser Verlag, 394p.
  • Çalışıcı H, Türkmen E, 2012. Modules that have a supplement in every cofinite extension, Georgian Math. J., 19, 209-216.
  • Kasch F, 1982. Modules and Rings, Second Edition, London New York, 384p.
  • Koşan MT, Harmancı A, 2005. Generalizations of coatomic modules, Cent. Eur. J. Math. 3(2), 273–281.
  • Koşan MT, 2007. lifting and supplemented modules, Algebra Colloq., 14(1), 53 - 60.
  • Özdemir S, 2013. Rad-supplementing modules, J. Korean Math. soc., 53(2), 403-408.
  • Sözen EÖ, Eren Ş, 2017. Modules that have a supplement in every extension, Eur. J. Pure App. Math.,10(4), 70-738.
  • Sözen EÖ, Eryılmaz F, Eren Ş, 2017. Modules that have a weak supplement in every torsion extension, Journal of Science and Arts, 39(2), 269-274.
  • Türkmen BN, 2015. Modules that have a supplement in every coatomic extension, Miskolc Math. Notes, 16(1), 543-551.
  • Tribak R, 2012. Finitely generated supplemented modules are amply supplemented , Bull. Aust. Math. Soc., 86(3), 430-439.
  • Ungör B, Halıcıoğlu S, Harmancı A, 2014. On a class of supplemented modules, Bull. Malays. Math. Sci. Soc., 37(3), 703-717.
  • Wang Y, 2007. small submodules and supplemented modules, Int. J. Math. Math. Sci., Article ID 58132, 8 p.
  • Wisbauer, R, 1991. Foundations of Modules and Rings, Gordon and Breach Science Publishers, Dusseldorff, 616p.
  • Zhou Y, 2000. Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq., 7(3), 305-318.
  • Zöschinger H, 1974. Moduln die in jeder Erweiterung ein Komplement haben, Math. Scand. 35, 267-287.
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Articles
Authors

Figen Eryılmaz

Publication Date June 27, 2019
Submission Date December 27, 2018
Published in Issue Year 2019

Cite

APA Eryılmaz, F. (2019). Her $\delta-$ Eşatomik Genişlemede $\delta-$ Tümleyene Sahip Modüller. Sinop Üniversitesi Fen Bilimleri Dergisi, 4(1), 47-53. https://doi.org/10.33484/sinopfbd.503751


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