Modules in which kernels of endomorphisms are invariant under all automorphisms

Quynh T. C., Chi N. T. D., KOŞAN M. T.

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

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0219498826502440
  • 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: duo ring, Kernel-invariant module, semicommutative ring, semiperfect ring
  • Gazi Üniversitesi Adresli: Evet

Özet

A right R-module M is called kernel-invariant (under automorphisms) if the kernels of all endomorphisms of M are invariant under all automorphisms of M. We show that the classes of kernel-invariant modules and rings inherit some of the important features of the aforementioned classes of modules and rings. For example, (1) Duo modules and uniform non-singular modules are kernel-invariant, (2) Endomorphism rings of kernel-invariant modules are kernel-invariant and they are abelian, (3) Domains are kernel-invariant which are not auto-invariant, (4) Semicommutative rings are kernel-invariant and the converse is true if they are clean.