KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

⊕-co-coatomically supplemented and co-coatomically semiperfect modules

Serpil GÜNGÖR
Rafail ALİZADE
Sayfa
1417–1426
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A ring is semiperfect if and only if every nitely generated free R-module is co-coatomically semiperfect.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper it is shown that a factor module of an ⊕-co-coatomically supplemented module is not in general ⊕-co-coatomically supplemented.
📊
Temel Bulgular & Veri:If M is⊕-co-coatomically supplemented and U is a fully invariant submodule of M, then M/U is ⊕-co-coatomically supplemented.
💡
Sonuç & Katkı:A ring is semiperfect if and only if every nitely generated free R-module is co-coatomically semiperfect.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper it is shown that a factor module of an ⊕-co-coatomically supplemented module is not in general ⊕-co-coatomically supplemented. If M is⊕-co-coatomically supplemented and U is a fully invariant submodule of M, then M/U is ⊕-co-coatomically supplemented. A ring R is left perfect if and only if R(N) is an ⊕-co-coatomically supplemented R-module. A projective module M is co-coatomically semiperfect if and only if M is ⊕-co-coatomically supplemented. A ring is semiperfect if and only if every nitely generated free R-module is co-coatomically semiperfect.

🔖

Bu Makaleye Atıf Yap

GÜNGÖR, S., ALİZADE, R. (2022). ⊕-co-coatomically supplemented and co-coatomically semiperfect modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1417–1426. https://ajindex.com/articles/529832

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. Alizade, R., Bilhan, G., and Smith, P. F. Modules whose maximal submodules have supplements. Communications in Algebra, 29(6):2389 2405, 2001.
  2. Anderson, F. and Fuller, K. Rings and Categories of Modules. Springer, 1992. B¸y¸ka³ k, E. and Lomp, C. Rings whose modules are weakly supplemented are perfect. applications to certain ring extensions. Mathematica Scandinavica, 105:25 30, 2009. Çal ³ c, H. and Pancar, A. -co nitely supplemented modules. Czechoslovak Math-ematical Journal, 54(129):1083 1088, 2004.
  3. Clark, J., Lomp, C., Vanaja, N., and Wisbauer, R. Lifting Modules. Birkh‰user Verlag, 2006.
  4. Fuchs, L. In nite Abelian Groups, Vol. I. New York: Academic Press, 1970.
  5. Idelhadj, A. and Tribak, R. A dual notion of cs-modules generalization. Algebra and Number Theory, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, 208:149 155, 2000.
  6. Idelhadj, A. and Tribak, R. On some properties of -supplemented modules. Inter-national Journal of Mathematics and Mathematical Sciences, 69:4373 4387, 2003.
  7. Kasch, F. Modules and Rings. London Mathematical Society, 1982.
  8. Keskin, D., Harmanc, A., and Smith, P. F. On -supplemented modules. Acta Mathematica Hungaria, 83(1-2):161 169, 1999.
  9. Keskin, D., Smith, P. F., and Xue, W. Rings whose modules are -supplemented. Journal of Algebra, 218:470 487, 1999.
  10. Mohamed, S. H. and M¸ller, B. J. Continuous and Discrete Modules. London Mathematical Society Lecture Notes Series, Cambridge Univ. Press,
  11. Cambridge, UK, 1990.
  12. Wang, Y. and Sun, Q. A note on -co nitely supplemented modules. International Journal of Mathematics and Mathematical Sciences, 2007:10836 5 pages, 2007.
  13. War eld Jr., R. B. Decomposability of nitely presented modules. Proceedings of the American Mathematical Society, 25(1):167 172, 1970.
  14. Wisbauer, R. Foundations of Modules and Rings. Gordon and Breach, 1991. Zˆschinger, H. Komplementierte moduln ¸ber dedekindringen. Journal of Algebra, 29:42 56, 1974. Zˆschinger, H. Moduln die in jeder erweiterung ein komplement haben. Mathematica Scandinavica, 35:267 287, 1974. Zˆschinger, H. and Rosenberg, F. A. Koatomare moduln. Mathematische Zeitschrift, 170(3):221 232, 1980