Commutative graded-n-coherent and graded valuation rings

Assarrar A., Mahdou N., TEKİR Ü., KOÇ S.

Hacettepe Journal of Mathematics and Statistics, cilt.51, sa.4, ss.1047-1057, 2022 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.947574
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1047-1057
  • Anahtar Kelimeler: coherent rings and modules, graded modules and rings, graded trivial extension ring, graded-coherent rings and modules, graded-valuation rings, n-coherent rings and modules
  • Marmara Üniversitesi Adresli: Evet

Özet

Let R = ⊕α∈GRα be a commutative ring with unity graded by an arbitrary grading commutative monoid G. For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced. In this paper many results are generalized from n-coherent rings to graded-n-coherent rings. In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.