On strongly dccr∗ modules

Naji O. A., Özen M., TEKİR Ü.

Journal of Algebra and its Applications, cilt.21, sa.10, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 10
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s021949882250195x
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Strongly dccr* modules, perfect rings, strongly special modules, Nakayama's Lemma, PRIME SUBMODULES, ACC
  • Marmara Üniversitesi Adresli: Evet

Özet

© 2022 World Scientific Publishing Company.In this paper, we introduce and study the concept of strongly dccr∗ modules. Strongly dccr∗ condition generalizes the class of Artinian modules and it is stronger than dccr∗ condition. Let R be a commutative ring with nonzero identity and M a unital R-module. A module M is said to be strongly dccr∗ if for every submodule N of M and every sequence of elements (ai) of R, the descending chain of submodules a1N ⊇ a1a2N ⊇ ⋯ ⊇ a1a2⋯anN ⊇⋯ of M is stationary. We give many examples and properties of strongly dccr∗. Moreover, we characterize strongly dccr∗ in terms of some known class of rings and modules, for instance in perfect rings, strongly special modules and principally cogenerately modules. Finally, we give a version of Union Theorem and Nakayama's Lemma in light of strongly dccr∗ concept.