Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON S-COHERENCE

  • Bennis, Driss (Centre de Recherche de Mathematiques et Applications de Rabat (CeReMAR) Faculty of Sciences Mohammed V University in Rabat) ;
  • El Hajoui, Mohammed (Centre de Recherche de Mathematiques et Applications de Rabat (CeReMAR) Faculty of Sciences Mohammed V University in Rabat)
  • Received : 2017.12.18
  • Accepted : 2018.04.24
  • Published : 2018.11.01
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Abstract

Recently, Anderson and Dumitrescu's S-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of S-finitely presented modules and then of S-coherent rings which are S-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an S-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other S-versions of finitely presented modules and coherent rings. We prove that these last S-versions can be characterized in terms of localization.

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References

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