Commutative graded-S-coherent rings

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

Czechoslovak Mathematical Journal, cilt.73, sa.2, ss.553-564, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.21136/cmj.2023.0130-22
  • Dergi Adı: Czechoslovak Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.553-564
  • Anahtar Kelimeler: 13A02, 13A15, 13D03, 16W50, graded-S-coherent module, graded-S-coherent ring, S-finite
  • Marmara Üniversitesi Adresli: Evet

Özet

Recently, motivated by Anderson, Dumitrescu’s S-finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of S-coherent rings, which is the S-version of coherent rings. Let R=⊕α∈GRα be a commutative ring with unity graded by an arbitrary commutative monoid G, and S a multiplicatively closed subset of nonzero homogeneous elements of R. We define R to be graded-S-coherent ring if every finitely generated homogeneous ideal of R is S-finitely presented. The purpose of this paper is to give the graded version of several results proved in D. Bennis, M. El Hajoui (2018). We show the nontriviality of our generalization by giving an example of a graded-S-coherent ring which is not S-coherent and as a special case of our study, we give the graded version of the Chase’s characterization of S-coherent rings.