## “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.

Ideal topologies

### Related Papers

 1. Faltings' finiteness dimension of local cohomology modules over local Cohen-Macaulay ringsCanad. Math. Bull. 60 (2017), 225-234  [abstract]
 2. A new proof of Faltings' local-global principle for the finiteness of local cohomology modulesArchiv der Mathematik (Accepted) [abstract]
 3. Cofiniteness with respect to ideals of small dimensionsAlgebr. Represent Theor. 18 (2015), 369-379  [abstract]
 4. R. Naghipour (joint with D. Asadollahi) Faltings' local-global principle for the finiteness of local cohomology modulesComm. 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 modulesComm. Algebra (2015), DOI: 10.1080/00927872.2013.843094  [abstract]
 6. On the generalization of Faltings' annihilator theoremArch. Math. (Basel) 102 (2014), 15-23  [abstract]
 7. Cofiniteness of torsion functors of cofinite modulesColloq. Math. 136 (2014), 221-230  [abstract]
 8. Cofiniteness of local cohomology modulesAlgebra Colloq. 21 (2014), 605-614  [abstract]
 9. A new characterization of Cohen-Macaulay ringsJ. Algebra Appl. 13 (2014), # 7 Pages  [abstract]
 10. A note on quintasymptotic prime idealsJ. Pure Appl. Algebra 218 (2014), 27-29  [abstract]
 11. On the finiteness of Bass numbers of local cohomology modules and cominimaxnessHouston J. Math. 40 (2014), 319-337  [abstract]
 12. Quintasymptotic sequences over an ideal and quintasymptotic cogradeBull. Iranian Math. Soc. (Accepted) [abstract]
 13. Minimaxness and cofinitemess properties of local cohomology modulesComm. Algebra 41 (2013), 2799-2814  [abstract]
 14. A note on minimal prime divisors of an idealAlgebra Colloq. (Accepted) [abstract]
 15. Cofiniteness of local cohomology modules for ideals of small dimensionJ. Algebra 321 (2009), 1997-2011  [abstract]
 16. Finiteness properties of local cohomology modules for a-minimax modulesProc. 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. Associated primes of local cohomology modules and matlis dualityJ. Algebra (Accepted) [abstract]
 19. Weakly GK-perfect and integral closure of idealsComm. Algebra (Accepted) [abstract]
 20. Asymptotic primes of Ratliff-Rush closure of ideals with respect to modulesComm. Algebra 36 (2008), 1942-1953  [abstract]
 21. Cohomological dimension of generalized local cohomology modulesAlgebra Colloq. 15 (2008), 303 - 308   [abstract]
 22. Integral closures, local cohomology and ideal topologiesRocky Mountain J. Math. 37 (2007), 905-916  [abstract]
 23. Asymptotic behavior of integral closures in modulesAlgebra Colloq. 14 (2007), 505 - 514   [abstract]
 24. Associated primes, integral closures and ideal topologiesColloq. Math. 105 (2006), 35-43  [abstract]
 25. Graded distributive modulesSoutheast Asian Bull. Math. 29 (2005), 1095-1099  [abstract]
 26. The Lichtenbaum-Hartshorne theorem for generalized local cohomology and connectednessComm. Algebra 30 (2002), 3687-3702  [abstract]
 27. Cohomological dimension of certain algebraic varietiesProc. Amer. Math. Soc. 130 (2002), 3537-3544  [abstract]
 28. Integral closure and ideal topologies in modulesComm. Algebra 29 (2001), 5239-5250  [abstract]
 29. Quintessential primes and ideal topologies over a moduleComm. Algebra 29 (2001), 3495-3506  [abstract]
 30. Locally unmixed modules and ideal topologiesJ. Algebra 236 (2001), 768-777  [abstract]
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