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Dergiler / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 17 Sayı: 1

On tau-discrete modules

Burcu Nişancı Türkmen(AMASYA ÜNİVERSİTESİ)0000-0001-7900-0529
Ergül Türkmen(AMASYA UNIVERSITY)0000-0002-7082-1176
Sayfa
37–43
Yayın Tarihi
2024-03-28
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is shown that: (1) direct summands of a (quasi) τ-discrete module are (quasi) τ-discrete; (2) a projective module M is τ-discrete iff M/(τ(M)) is semisimple and τ(M) is QSL; (3) if a projective module M is Soc-lifting, then M/(Soc(M)) is Soc-discrete and Rad(M/Soc(M) ) is semisimple.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:An R-module M is said to be (quasi) τ-discrete if M is τ-lifting and has the property (D_2) (respectively, has the property (D_3)), where τ is a preradical in R-mod.
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Temel Bulgular & Veri:An R-module M is said to be (quasi) τ-discrete if M is τ-lifting and has the property (D_2) (respectively, has the property (D_3)), where τ is a preradical in R-mod.
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Sonuç & Katkı:It is shown that: (1) direct summands of a (quasi) τ-discrete module are (quasi) τ-discrete; (2) a projective module M is τ-discrete iff M/(τ(M)) is semisimple and τ(M) is QSL; (3) if a projective module M is Soc-lifting, then M/(Soc(M)) is Soc-discrete and Rad(M/Soc(M) ) is semisimple.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:preradical · τ-lifting mdule · (quasi) τ-discrete module.

Abstract

An R-module M is said to be (quasi) τ-discrete if M is τ-lifting and has the property (D_2) (respectively, has the property (D_3)), where τ is a preradical in R-mod. It is shown that: (1) direct summands of a (quasi) τ-discrete module are (quasi) τ-discrete; (2) a projective module M is τ-discrete iff M/(τ(M)) is semisimple and τ(M) is QSL; (3) if a projective module M is Soc-lifting, then M/(Soc(M)) is Soc-discrete and Rad(M/Soc(M) ) is semisimple.

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Bu Makaleye Atıf Yap

Türkmen, B. N., Türkmen, E. (2024). On tau-discrete modules. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 17 Sayı: 1, 37–43. https://doi.org/10.18185/erzifbed.1251658

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Kaynakça (9)

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  2. Al-Takhman, K., Lomp, C. and Wisbauer, R. (2006) τ-complement and τ-supplement submodules, Algebra and Discrete Mathematics, 3, 1-15.
  3. Alkan, M. (2009) On τ-lifting modules and τ-semiperfect modules, Turkish Journal of Mathematics, 33(2), 117-130.
  4. Büyükaşık, E., Mermut, E. and Özdemir, S. (2010) Rad-supplemented modules, Rendiconti del Seminario Matematico della Universita di Padova, 124, 157-177.
  5. Mohamed S.H. and Müller, B.J. (1990) Continuous and Discrete Modules”, London Mathematical Society, LNS 147 Cambridge University Press, Cambridge.
  6. 6] Nicholson, W.K. and Zhou, Y. (2005) Strongly lifting, Journal of Algebra, 285, 795-818.
  7. Nişancı Türkmen, B., Ökten, H.H. and Türkmen, E. (2021) Rad-discrete Modules, Bulletin of the Iranian Mathematical Society, 47, 91-100.
  8. Türkmen, E. (2013) Rad-⨁-supplemented modules”, Analele Stiintifice ale Universitatii Ovidius Constanta Seria Mathematica, 21 (1), 225-238.
  9. Wisbauer, R. (1991) Foundations of Module and Ring Theory (A handbook for study and research)”, Gordon and Breach Science Publishers.