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Dergiler / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 3

When $delta$-semiperfect rings are semiperfect

Engin BÜYÜKAŞIK
Christian LOMP
Sayfa
317–324
Yayın Tarihi
2022-11-05
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Module theoretic version of our results are obtained.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Zhou defined δ -semiperfect rings as a proper generalization of semiperfect rings.
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Temel Bulgular & Veri:The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the semilocal rings which are δ -supplemented.
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Sonuç & Katkı:Module theoretic version of our results are obtained.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Zhou defined δ -semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the semilocal rings which are δ -supplemented. Module theoretic version of our results are obtained.

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Bu Makaleye Atıf Yap

BÜYÜKAŞIK, E., LOMP, C. (2022). When $delta$-semiperfect rings are semiperfect. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 3, 317–324. https://ajindex.com/articles/608538

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Kaynakça (8)

  1. Al-Takhman, K.: Cofinitely δ -supplemented and Cofinitely δ -semiperfect modules. Int. J. Algebra. 1(12), 601-613 (2007)
  2. Alizade, R., Bilhan, G., Smith, P. F.: Modules whose maximal submodules have supplements. Comm. Algebra. 29, 2389-2405 (2001)
  3. Anderson, F. W., Fuller, K. R.: Rings and categories of modules. New York. Springer 1992
  4. Bass, H.: Finitistic dimension and a homological generalization of semiprimary rings. Trans. Amer. Math. Soc. 95, 466–488 (1960)
  5. Kasch, F., Mares, E. A.: Eine Kennzeichnung semi-perfekter Moduln. Nagoya Math. J. 27, 525-529 (1966)
  6. Ko¸san, M. T.: δ -lifting and δ -supplemented modules. Algebra Colloq. 14(1), 53-60 (2007)
  7. Wisbauer, R.: Foundations of Modules and Rings. Gordon and Breach 1991
  8. Zhou, Y.: Generalizations of perfect, semiperfect and semiregular rings. Algebra Colloq. 7(3), 305-318 (2000).