On Divided Modules

TEKİR Ü., Ulucak G., KOÇ S.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.44, ss.265-272, 2020 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s40995-020-00827-1
  • Dergi Adı: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Agricultural & Environmental Science Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Communication Abstracts, zbMATH
  • Sayfa Sayıları: ss.265-272
  • Anahtar Kelimeler: Divided ring, Divided module, Trivial extension
  • Marmara Üniversitesi Adresli: Evet

Özet

Recall that a commutative ring R is said to be a divided ring if its each prime ideal P is comparable with each principal ideal (a), where a is an element of R. In this paper, we extend the notion of divided rings to modules in two different ways: let R be a commutative ring with identity and M a unital R-module. Then M is said to be a divided (weakly divided) module if its each prime submodule N of M is comparable with each cyclic submodule Rm (rM) of M, where m is an element of M (r is an element of R). In addition to give many characterizations of divided modules, some topological properties of (quasi-) Zariski topology of divided modules are investigated. Also, we study the divided property of trivial extension R proportional to M.