Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On the Local Cohomology and Formal Local Cohomology Modules

  • Shahram Rezaei (Department of Mathematics, Payame Noor University (PNU)) ;
  • Behruz Sadeghi (Department of Mathematics, Payame Noor University (PNU))
  • Received : 2022.07.31
  • Accepted : 2023.01.17
  • Published : 2023.03.31
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Abstract

Let 𝔞 and 𝔟 be ideals of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d > 0. We prove some results concerning the top local cohomology and top formal local cohomology modules. Among other things, we determine SuppR(𝔟 Hd𝔞(M)) and SuppR(𝔟𝔉d𝔞(M)). Also, we obtain some relations between AnnR(𝔟 Hd𝔞(M)), AttR(𝔟 Hd𝔞(M)) and SuppR(𝔟 Hd𝔞(M)) and we get similar results for 𝔟𝔉d𝔞(M).

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Acknowledgement

The author would like to thank the referee for careful reading and many useful suggestions.

References

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