Abstract
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)≅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≅U d (M) will be given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banica, C., Soia, M.: Singular sets of a module on local cohomology. Boll. Unione Mat. Ital, B 16, 923–934 (1976)
Brodmann, M.P., Sharp, R.Y.: Local Cohomology: An Algebraic Introduction with Geometric Applications. Cambridge University Press, Cambridge (1998)
Grothendieck, A.: Local Cohomology. Lect. Notes Math., vol. 41. Springer, New York (1966)
Herzog, J., Kunz, E.: Der Kanonische Modul Eines Cohen–Macaulay Rings. Lect. Notes Math., vol. 238. Springer, Berlin (1971)
Matsumura, H.: Commutative Ring Theory. Cambridge University Press, Cambridge (1986)
Rotman, J.J.: An Introduction to Homological Algebra. Academic Press, New York (1979)
Zamani, N., Bijan-Zadeh, M.H., Sayedsadeghi, M.S.: Cohomology with supports of dimension ≤d. Submitted
Acknowledgements
We would like to thank the referees for their careful reading of the manuscript and offering useful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zamani, N., Bijan-Zadeh, M.H. & Sayedsadeghi, M.S. d-Transform Functor and Some Finiteness and Isomorphism Results. Vietnam. J. Math. 42, 179–186 (2014). https://doi.org/10.1007/s10013-013-0042-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10013-013-0042-2