On regular fusible modules

Naji O. A., Özen M., TEKİR Ü., KOÇ S.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, cilt.119, sa.1, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 119 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s13398-024-01679-9
  • Dergi Adı: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: 16D10, 16D80, 16U99, Fusible module, Fusible ring, Regular fusible module, Regular fusible ring, Regular fusible submodule
  • Marmara Üniversitesi Adresli: Evet

Özet

In this article, we introduce the notion of regular fusible modules. Let R be a ring with an identity and M an R-module. An element 0≠m∈M is said to be regular fusible if there exist r∈R, a non zero-divisor of M, such that mr can be written as the sum of a torsion element and a torsion free element in M. M is called regular fusible if every nonzero element of M is regular fusible. We characterize regular fusible modules in terms of fusible modules. In addition, we show that a regular fusible module over a right duo ring is reduced and nonsingular. Moreover, we study the regular fusible property under Cartesian product, trivial extension ring, and module of fractions. Also, we characterize division rings in terms of fusible modules.