Bulletin of the Korean Mathematical Society (대한수학회보)

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COMINIMAXNESS WITH RESPECT TO IDEALS OF DIMENSION ONE

  • Irani, Yavar (Department of Mathematics Islamic Azad University Meshkin-Shahr Branch)
  • Received : 2016.02.03
  • Published : 2017.01.31
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Abstract

Let R denote a commutative Noetherian (not necessarily local) ring and let I be an ideal of R of dimension one. The main purpose of this note is to show that the category ${\mathfrak{M}}(R,\;I)_{com}$ of I-cominimax R-modules forms an Abelian subcategory of the category of all R-modules. This assertion is a generalization of the main result of Melkersson in [15]. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category ${\mathcal{C}}^1_B(R)$ of all R-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all R-modules.

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References

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