Goldie extending property on the class of exact submodules

TERCAN A., YAŞAR R., Yücel C. C.

Communications in Algebra, cilt.50, sa.4, ss.1363-1371, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/00927872.2021.1980580
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1363-1371
  • Anahtar Kelimeler: ES-module, exact submodule, Goldie-extending module, left exact preradical, rational hull
  • Ankara Üniversitesi Adresli: Hayır

Özet

We define a module M to be (Formula presented.) -extending if for each exact submodule X of M there exists a direct summand D of M such that (Formula presented.) is essential in both X and D. We investigate (Formula presented.) -extending modules and locate the implications between the other extending properties. We study decomposition theory and extensions for (Formula presented.) -extending concept. We show that if a ring is right (Formula presented.) -extending, then so its essential overring. It is shown that (Formula presented.) -extending property is inherited by its rational hull. We provide examples by making special choices of left exact preradicals.