MODULES WITH THE PROPERTY Rad(g)

Eryılmaz F., TÜRKMEN B. N.

JOURNAL OF SCIENCE AND ARTS, sa.4, ss.821-828, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2022
  • Doi Numarası: 10.46939/j.sci.arts-22.4-a04
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.821-828
  • Anahtar Kelimeler: g-radical supplement, extension, SSI-ring, semisimple commutative ring, SUPPLEMENT
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this article, we introduce modules with the property Rad(g) and provide various properties of this module. Firstly, we prove that every semisimple module has the property Rad(g). We also indicate that the class of modules with the property Rad(g) is closed under finite direct sum and direct summands. Moreover, we define the concepts of g (radical) cover. We show that factor modules of a module with the property Radg have the property Rad(g) under special condition. Additionally, we characterize semisimple commutative rings via modules with the property Rad(g).