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]