Cofinitely Goldie*-Supplemented Modules

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Güroğlu A. T.

Journal of New Theory, sa.43, ss.35-42, 2023 (Hakemli Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: Sayı: 43
  • Basım Tarihi: 2023
  • Doi Numarası: 10.53570/jnt.1260505
  • Dergi Adı: Journal of New Theory
  • Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.35-42
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

One of the generalizations of supplemented modules is the Goldie*-supplemented module, defined by Birkenmeier et al. using β∗ relation. In this work, we deal with the con- cept of the cofinitely Goldie*-supplemented modules as a version of Goldie*-supplemented module. A left R-module M is called a cofinitely Goldie*-supplemented module if there is a supplement submodule S of M with Cβ∗S, for each cofinite submodule C of M . Evi- dently, Goldie*-supplemented are cofinitely Goldie*-supplemented. Further, if M is cofinitely Goldie*-supplemented, then M/C is cofinitely Goldie*-supplemented, for any submodule C of M . If A and B are cofinitely Goldie*-supplemented with M = A ⊕ B, then M is cofinitely Goldie*-supplemented. Additionally, we investigate some properties of the cofinitely Goldie*- supplemented module and compare this module with supplemented and Goldie*-supplemented modules.