On weakly 1-absorbing primary submodules

Yetkin Çelikel E., Koç S., Tekir Ü., Yıldız E.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.22, sa.1, ss.1-17, 2024 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 1
  • Basım Tarihi: 2024
  • 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
  • Sayfa Sayıları: ss.1-17
  • Marmara Üniversitesi Adresli: Evet

Özet

Abstract

In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let R" role="presentation" >R be a commutative ring with a nonzero identity and M" role="presentation" >M be a nonzero unital module. A proper submodule N" role="presentation" >N of M" role="presentation" >M is said to be a weakly 1-absorbing primary submodule if whenever 0≠abm∈N" role="presentation" >0≠abm∈N for some nonunit elements a,b∈R" role="presentation" >a,b∈R and m∈M," role="presentation" >m∈M, then ab∈(N:M)" role="presentation" >ab∈(N:M) or m∈M" role="presentation" >m∈M-rad(N)," role="presentation" >rad(N), where M" role="presentation" >M-rad(N)" role="presentation" >rad(N) is the prime radical of N." role="presentation" >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.