Results on special cohomology modules with bounded support

Document Type : Original Paper

Authors

1 payame noor university, Tehran, Iran

2 payame noor university (PNU), P> O. Box 19395-4697, Tehran, Iran

3 payame noor university (PNU), P> O. Box 19395-4697, Tehran, Iran

10.22055/jamm.2025.20016

Abstract

Let R be a commutative with identity and Noetherian ring, J an ideal of R and let d a non-negative integer. For R-module M, Γd,J (M) containing the x of M satisfying Ix ⊆ Jx, for some ideals of R such as I with condition dimR(R/I) ≤ d. In this paper, inspired by this module, for R modules M and N, we define the submodule (d, J)-torsion Γd,J (M, N) of HomR(M, N) and for any non-negative integer i, denote its i-th right derived functor by Hid,J (M, −) and study some of its features. Also, by defining the W(d, J), W( ˜ d, J) sets of ideals, we express and prove theorems about the associated prime ideals of Hid,J(M,N). Finally, we show under the condition that Hid,J(M, N) = 0.Let R is a commutative Noetherian and ring, J is an ideal of R and d is an integer and be non-negative. For R−the module M,) M (J,Γd contains all xof M that in The condition Jx ⊆ Ix applies to some ideals I of R with singularity d) ≤ I/R(dim). In this article, inspired by this module, for R− modules M and N, submodule J, d We define (N,M(J,Γd) from (N,M(HomR) and for each non-negative integer i, i−Hi show some features Its right derived functor is denoted by (−,M(J,d We study it. Also, by defining ideal sets (J,d(W and Hi expressed and (J ,d( ˜ W Hi We prove. Finally, under the conditions we show that 0 =(N,M (J,d.

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References

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History

  • Receive Date: 07 March 2024
  • Revise Date: 26 January 2025
  • Accept Date: 06 April 2025

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