Actions of R-module groupoids

ÖZCAN A. F., İÇEN İ.

Filomat, cilt.37, sa.13, ss.4239-4247, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 13
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2298/fil2313239o
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4239-4247
  • Anahtar Kelimeler: action of groupoid, ℜ-module groupoid
  • İnönü Üniversitesi Adresli: Evet

Özet

Let R be a ring, 1R be the identity of ring R and N be an R-module on R. In this work, we are going to give a new definition that it is called an action of R-module groupoids. First, we are going to give the definition of the action of the R-module groupoids on the R-module N. Then we obtained a new category RMGpdOp(Ω) of actions of Ω on R-modules. We also find that there is a groupoid Ω ▷◁ N on N. Ω ▷◁ N is called action R-module groupoid. Finally, we prove that the category RMGpdOp(Ω) of actions of R-module groupoids is equivalent to RMGpdCov(Ω) of coverings of R-module groupoids.