On S-multiplication modules

Anderson D., Arabaci T., TEKİR Ü., KOÇ S.

Communications in Algebra, cilt.48, sa.8, ss.3398-3407, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 8
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1080/00927872.2020.1737873
  • 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.3398-3407
  • Anahtar Kelimeler: multiplication module, prime submodule, S-multiplication module, S-prime submodule
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

In this article, we introduce S-multiplication modules which are a generalization of multiplication modules. Let M be an R-module and (Formula presented.) a multiplicatively closed subset. M is said to be an S-multiplication module if for each submodule N of M there exist (Formula presented.) and an ideal I of R such that (Formula presented.) Besides giving many properties of S-multiplication modules, we generalize some results on multiplication modules to S-multiplication modules. Also, we study S-prime submodules in S-multiplication modules. In particular, we generalize prime avoidance lemma for multiplication modules to S -multiplication modules. Furthermore, we characterize multiplication modules in terms of S-multiplication modules. Communicated by Toma Albu.