“Reza Naghipour”

Tel:  (+98)(411)3392875
Fax:  (+98)(411)3342102
Email: 

IPM Positions

Non Resident Researcher (non-resident), School of Mathematics
(2009 - 2012
(From December 2009))

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics
(2006 - 2009)
Associate Researcher (non-resident), School of Mathematics
(2005 - 2006)

Associate Researcher (non-resident), School of Mathematics
(2001 - 2003)


Non IPM Affiliations

Professor of Tabriz University

Research Activities

Let R be a commutative Noertherian ring, and N a finitely generated R- module. For an ideal I of R and a submodule M of N the increasing sequence of submodules
?

M ? M:NI ? M:NI2 ? ... ? M:NIn ? ...

becomes stationary. Denote its ultimate constant value by M:N?I?. Note that M:N?I? for all large n. Let I ? J be two ideals of R, and let S be a multiplicatively closed subset of R. For a submodule M of N, we use S(M) to denote the submodule ?s ? S(M:Ns). Note that the primary decomposition of S(M) consists of the intersection of all primary components of M whose associated prime ideals do not meet S. Also, if R is a domain with field of fractions K, and that N is a torsion-free R-module, an element v ? N?RK is said to be integral over N if v ? NV for every discrete valuation ring V of K containing R. The Rees integral closure of N is the set of all elements of NK that are integral over N, and is denoted by [`N]. The integral closure of M in N, denoted by Ma, is the submodule Ma:=[`M]?N, where [`M] denotes the Rees integral closure of M. It is shown that, under certain additional assumptions, the topology defined by InN, is weaker than the topology defined by InN:N?I? . Second, S- symbolic topology S((InN)a) , is compared with another well - defined topology, where (InN)a denotes the integral closure of InN in N.

Present Research Project at IPM

Ideal topologies

Related Papers

1. K. Bahmanpour and R. Naghipour
Faltings' finiteness dimension of local cohomology modules over local Cohen-Macaulay rings
Canad. Math. Bull. 60 (2017), 225-234  [abstract]
2. R. Naghipour (Joint with D. Asadollahi)
A new proof of Faltings' local-global principle for the finiteness of local cohomology modules
Archiv der Mathematik (Accepted) [abstract]
3. K. Bahmanpour and R. Naghipour (Joint with M. Sedghi)
Cofiniteness with respect to ideals of small dimensions
Algebr. Represent Theor. 18 (2015), 369-379  [abstract]
4. R. Naghipour (joint with D. Asadollahi)
Faltings' local-global principle for the finiteness of local cohomology modules
Comm. Algebra (2015), DOI:10.1080/00927872.2013.849261  [abstract]
5. R. Naghipour (Joint with M. R. Doustimehr)
Faltings' local-global principle for the minimaxness of local cohomology modules
Comm. Algebra (2015), DOI: 10.1080/00927872.2013.843094  [abstract]
6. R. Naghipour (Joint with M. R. Doustimehr)
On the generalization of Faltings' annihilator theorem
Arch. Math. (Basel) 102 (2014), 15-23  [abstract]
7. R. Naghipour and K. Bahmanpour (Joint with I. Khalili Gorji)
Cofiniteness of torsion functors of cofinite modules
Colloq. Math. 136 (2014), 221-230  [abstract]
8. K. Bahmanpour and R. Naghipour (Joint with M. Sedghi)
Cofiniteness of local cohomology modules
Algebra Colloq. 21 (2014), 605-614  [abstract]
9. K. Bahmanpour and R. Naghipour
A new characterization of Cohen-Macaulay rings
J. Algebra Appl. 13 (2014), # 7 Pages  [abstract]
10. R. Naghipour (Joint with S. Jahandoust)
A note on quintasymptotic prime ideals
J. Pure Appl. Algebra 218 (2014), 27-29  [abstract]
11. K. Bahmanpour and R. Naghipour (Joint with M. Sedghi)
On the finiteness of Bass numbers of local cohomology modules and cominimaxness
Houston J. Math. 40 (2014), 319-337  [abstract]
12. R. Naghipour (joint with S. Jahandoust)
Quintasymptotic sequences over an ideal and quintasymptotic cograde
Bull. Iranian Math. Soc. (Accepted) [abstract]
13. K. Bahmanpour and R. Naghipour (Joint with M. Sedghi)
Minimaxness and cofinitemess properties of local cohomology modules
Comm. Algebra 41 (2013), 2799-2814  [abstract]
14. R. Naghipour (K. Bahmanpour and A. Khojali)
A note on minimal prime divisors of an ideal
Algebra Colloq. (Accepted) [abstract]
15. R. Naghipour (Joint with K. Bahmanpour)
Cofiniteness of local cohomology modules for ideals of small dimension
J. Algebra 321 (2009), 1997-2011  [abstract]
16. R. Naghipour (Joint with J. Azami and B. Vakili)
Finiteness properties of local cohomology modules for a-minimax modules
Proc. Amer. Math. Soc. 137 (2009), 439-448  [abstract]
17. N. Tajbakhsh, B. Nadjar Arabi and H. Soltanianzadeh
An Intelligent Decision Combiner Applied to Noncooperative Iris Recognition
( In: Presented at and Published in the Proceeding of the 11th International Conference on Information Fusion, Cologne, Germany, June 30-July 3, 2008)
[abstract]
18. R. Naghipour (Joint with K. Bahmanpour)
Associated primes of local cohomology modules and matlis duality
J. Algebra (Accepted) [abstract]
19. R. Naghipour (J. Azami and B. Vakili)
Weakly GK-perfect and integral closure of ideals
Comm. Algebra (Accepted) [abstract]
20. R. Naghipour (Joint with J. Amjadi)
Asymptotic primes of Ratliff-Rush closure of ideals with respect to modules
Comm. Algebra 36 (2008), 1942-1953  [abstract]
21. R. Naghipour (Joint with J. Amjadi)
Cohomological dimension of generalized local cohomology modules
Algebra Colloq. 15 (2008), 303 - 308   [abstract]
22. R. Naghipour
Integral closures, local cohomology and ideal topologies
Rocky Mountain J. Math. 37 (2007), 905-916  [abstract]
23. R. Naghipour (Joint with P. Schenzel)
Asymptotic behavior of integral closures in modules
Algebra Colloq. 14 (2007), 505 - 514   [abstract]
24. R. Naghipour
Associated primes, integral closures and ideal topologies
Colloq. Math. 105 (2006), 35-43  [abstract]
25. R. Naghipour (Joint with N. Zamani)
Graded distributive modules
Southeast Asian Bull. Math. 29 (2005), 1095-1099  [abstract]
26. R. Naghipour, K. Divaani-Aazar and M. Tousi
The Lichtenbaum-Hartshorne theorem for generalized local cohomology and connectedness
Comm. Algebra 30 (2002), 3687-3702  [abstract]
27. K. Divaani-Aazar, R. Naghipour and M. Tousi
Cohomological dimension of certain algebraic varieties
Proc. Amer. Math. Soc. 130 (2002), 3537-3544  [abstract]
28. K. Divaani-Aazar and R. Naghipour
Integral closure and ideal topologies in modules
Comm. Algebra 29 (2001), 5239-5250  [abstract]
29. R. Naghipour
Quintessential primes and ideal topologies over a module
Comm. Algebra 29 (2001), 3495-3506  [abstract]
30. R. Naghipour
Locally unmixed modules and ideal topologies
J. Algebra 236 (2001), 768-777  [abstract]
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