On Bassian and generalized Bassian modules

Das S., KOŞAN M. T., Taşdemi̇R Ö., Žemlička J.

Journal of Algebra and its Applications, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0219498826502750
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: (Generalized) Bassian group, (Generalized) Bassian module, Abelian group, Hopfian group, Hopfian module
  • Gazi Üniversitesi Adresli: Evet

Özet

A right R-module M is called (generalized) Bassian if the existence of an injective homomorphism M → M/N for some submodule N of M implies that N = {0} (N is a direct summand of M). We partially describe relationships between the classes of Bassian and generalized Bassian modules. In particular, we show that generalized Bassian abelian groups are precisely direct sums of Bassian and semisimple abelian groups, which is a positive answer for Conjecture 1.3 in [P. V. Danchev and P. W. Keef, Generalized Bassian and other mixed abelian groups with bounded p-torsion, J. Algebra 663(1) (2025) 1–19].