d-Transform Functor and Some Finiteness and Isomorphism Results

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• 作者：Naser Zamani (1)
  M. H. Bijan-Zadeh (2)
  M. S. Sayedsadeghi (3)
  
• 关键词：Biequidimensional rings ; d ; Local cohomology ; d ; Transform functor ; 13A30 ; 13A99 ; 13D45
• 刊名：Vietnam Journal of Mathematics
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：42
• 期：2
• 页码：179-186
• 全文大小：
• 参考文献：1. Banica, C., Soia, M.: Singular sets of a module on local cohomology. Boll. Unione Mat. Ital, B 16, 923-34 (1976)
  2. Brodmann, M.P., Sharp, R.Y.: Local Cohomology: An Algebraic Introduction with Geometric Applications. Cambridge University Press, Cambridge (1998) CrossRef
  3. Grothendieck, A.: Local Cohomology. Lect. Notes Math., vol. 41. Springer, New York (1966)
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  5. Matsumura, H.: Commutative Ring Theory. Cambridge University Press, Cambridge (1986)
  6. Rotman, J.J.: An Introduction to Homological Algebra. Academic Press, New York (1979)
  7. Zamani, N., Bijan-Zadeh, M.H., Sayedsadeghi, M.S.: Cohomology with supports of dimension ?em class="a-plus-plus">d. Submitted
  
• 作者单位：Naser Zamani (1)
  M. H. Bijan-Zadeh (2)
  M. S. Sayedsadeghi (3)
  
  1. Faculty of Mathematical Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran
  2. Faculty of Mathematics and Computer Science, Tehran Teacher Training University, Tehran, Iran
  3. Department of Mathematics, Faculty of Science, Payame Noor University (PNU), Tehran, Iran
  
• ISSN：2305-2228

文摘

Let R be a Noetherian ring, M be an R-module and let d be a non-negative integer. We introduce the R-module U d (M) and the functor T d (? on the category of R-modules. General concerning results on the module T d (M) and its relationship with d-local cohomology modules \(H^{i}_{d}(M)\) will be given. Then, whenever M is finitely generated, under a mild condition we show that T d (M)?em class="a-plus-plus">U d (M), which turns out a result on the finiteness of the set \(\operatorname{Ass}_{R}(T_{d}(M))\) . Finally a criterion for the isomorphism M?em class="a-plus-plus">U d (M) will be given.