On weakly 1-absorbing primary submodules

Çelikel E. Y., KOÇ S., TEKİR Ü., YILDIZ YILMAZ E.

Journal of Algebra and its Applications, vol.23, no.2, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1142/s0219498824500361
  • Journal Name: Journal of Algebra and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: (weakly) primary-like submodule, 1-absorbing primary submodule, simple module, weakly 1-absorbing primary submodule, Weakly prime submodule
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let R be a commutative ring with a nonzero identity and M be a nonzero unital module. A proper submodule N of M is said to be a weakly 1-absorbing primary submodule if whenever 0 /= abm ϵ N for some nonunit elements a, b ϵ R and m ϵ M, then ab ϵ (N : M) or m ϵ M-rad(N), where M-rad(N) is the prime radical of N. Many properties and characterizations of weakly 1-absorbing primary submodules are given. We also give the relations between weakly 1-absorbing primary submodules and other classical submodules such as weakly prime, weakly primary, weakly 2-absorbing primary submodules. Also, we use them to characterize simple modules.