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.
Keywords
$\delta-$ eşatomik genişleme $\delta-$-E*-modül $\delta-$-EE*-modül $\delta-$-mükemmel halka
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.
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.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 27, 2019 |
| Submission Date | December 27, 2018 |
| Published in Issue | Year 2019 Volume: 4 Issue: 1 |
