IPM Positions

Non Resident Researcher (non-resident), School of Mathematics (2010 - 2013 )

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics (2006 - 2008) (Until June ) Associate Researcher (non-resident), School of Mathematics (2002 - 2006) Associate Researcher, School of Mathematics (1999 - 2002)

Non IPM Affiliations

Professor of Ferdowsi University of Mashad

Research Interests

Local cohomology models, Associated prime ideal of local cohomology models, d-sequences, Filter regular sequences, Flat cover of models

Research Activities

1 Let R be a commutative Noetherian local ring with maximal ideal \frakm. It is well known that the class of modules of finite projective dimension characterizes regular rings in the following precise sense: R is regular ? p.dim M < ? for every R-module M ? p.dim k < ? where k=R/\frakm. Auslander and Briger, introduced a notion of Gorenstein dimension. It has the same relation to the Gorenstein properties of R as the projective dimension has to its regularity. In this research by using the notion of Gorenstein dimension, we study the finiteness properties of local cohomology modules. Footnotes: 1*Project number: 81130021 2. Tight closure Tight closure introduced by M. Hochster and C.Huneke in late 1986 .Tight closure is a closure operation performed on ideals in a commutative, Noetherian ring of prime characteristic. Although it has many important applications to commutative algebra and related areas, some basic questions about tight closure remain open. One of the biggest such open problems is whether or not tight closure commutes with localization. Let R denote a Noetherian commutative ring of prime characteristic. We say that tight closure commutes with localization in R if, for all ideals I in R and all multiplicative systems U in R , ?I*(U-1R) = (IU-1R)*.

Present Research Project at IPM

Gorenstein dimension and finiteness properties of local cohomology modules*

More Information

Please make a link to my papers.

Related Papers

1.	M. Nasernejad and K. Khashyarmanesh On the Alexander dual of the path ideals of rooted and unrooted trees Comm. Algebra (Accepted) [abstract]

2.	K. Khashyarmanesh and M. Afkhami (Joint with Z. Barati) When the unit, unitary and total graphs are ring graphs and outerplanar Rocky Mountain J. Math. (2014), DOI: 10.1216/RMJ-2014-44-2-1  [abstract]

3.	M. Afkhami and K. Khashyarmanesh (Joint with Z. Barati) Cayley graphs of partially ordered sets J. Algebra Appl. 12 (2013), # P 13  [abstract]

4.	M. Afkhami and K. Khashyarmanesh (Joint with Z. Barati) When the comaximal and zero-divisor graphs are ring graphs and outerplanar Rocky Mountain J. Math. (Accepted) [abstract]

5.	M. Afkhami and K. Khashyarmanesh (Joint with M. Farrokhi) Planar, outerplanar and ring graph cozero-divisor graphs Ars Combin. 11 (2012), #9 Pages  [abstract]

6.	M. Afkhami and K. Khashyarmanesh Planar, outerplanar, and ring graph of the cozero-divisor graph of a finite commutative ring J. Algebra Appl. (Accepted) [abstract]

7.	K. Khashyarmanesh (Joint with F. Khosh-Ahang) On the behavior of applying derived functors of torsion functors on local cohomology modules J. Algebra Appl. (Accepted) [abstract]

8.	K. Khashyarmanesh (Joint with F. Khosh-Ahang) On the annihilators of derived fuctors of local cohomology modules and finiteness dimension Comm. Algebra (Accepted) [abstract]

9.	K. Khashyarmanesh On the endomorphism rings of local cohomology modules Canad. Math. Bull. (Accepted) [abstract]

10.	K. Khashyarmanesh On the finiteness properties of associated primes of generalized local cohomology modules Forum Math. 20 (2008), 265–273  [abstract]

11.	K. Khashyarmanesh (Joint with F. Khosh-Ahang) Asymptotic behaviour of certain sets of associated prime ideals of EXT-modules Manuscripta Math. (Accepted) [abstract]

12.	K. Khashyarmanesh On the uniform behaviour of the Frobenius closures of ideals Colloq. Math. 109 (2007), 1-7  [abstract]

13.	K. Khashyarmanesh (Joint with A. Abbasi) Gorenstein injective dimension of generalized local cohomology modules Ital. J. pure Appl. Math. (Accepted) [abstract]

14.	K. Khashyarmanesh On the matlis duals of local cohomology modules Archiv der Mathematik 88 (2007), 413-418  [abstract]

15.	K. Khashyarmanesh (Joint with A. Abbasi) On the asymptotic behaviour of associated primes of generalized local cohomology modules J. Aust. Math. Soc. 83 (2007), 217–225  [abstract]

16.	K. Khashyarmanesh On the finiteness properties of extension and torsion fuctors of local cohomology modules Proc. Amer. Math. Soc. (Accepted) [abstract]

17.	K. Khashyarmanesh On the finiteness properties of ∪iAssRExtnR(R/\frakai, M) Comm. Algebra 34 (2006), 779 – 784   [abstract]

18.	K. Khashyarmanesh and Sh. Salarian Uniform annihilation of local cohomology modules over a Gorenstein ring Comm. Algebra 34 (2006), 1625 – 1630   [abstract]

19.	K. Khashyarmanesh Associated primes of graded components of generalized local cohomology modules Comm. Algebra 33 (2005), 3081 – 3090   [abstract]

20.	K. Khashyarmanesh A surjective homomorphism of local cohomology modules Comm. Algebra 33 (2005), 2717 – 2723   [abstract]

21.	K. Khashyarmanesh and M. Yassi On the finiteness properties of generalized local cohomological modules Algebra Colloq. 12 (2005), 293-300  [abstract]

22.	K. Khashyarmanesh, M. Yassi and A. Abbasi A new version of Local-Global Principle for annihilations of local cohomology modules Colloq. Math. 100 (2004), 213-219  [abstract]

23.	K. Khashyarmanesh and Sh. Salarian Faltings' theorem for the annihilation of local cohomology modules over a Gorenstein ring Proc. Amer. Math. Soc. 132 (2004), 2215-2220   [abstract]

24.	K. Khashyarmanesh, M. Yassi and A. Abbasi Filter regular sequences and generalized local cohomology modules Comm. Algebra 32 (2004), 253-259  [abstract]

25.	K. Khashyarmanesh and Sh. Salarian On the rings whose injective hulls are flat Proc. Amer. Math. Soc. 131 (2003), 2329-2335   [abstract]

26.	J. Asadollahi, K. Khashyarmanesh and Sh. Salarian A generalization of the cofiniteness problem in local cohomology modules J. Aust. Math. Soc. 75 (2003), 313-324  [abstract]

27.	J. Asadollahi, K. Khashyarmanesh and Sh. Salarian On the minimal flat resolutions of modules Comm. Algebra 30 (2002), 3813-3823  [abstract]

28.	K. Khashyarmanesh and Sh. Salarian A finiteness result for local cohomology modules Comm. Algebra 30 (2002), 3821-4826  [abstract]

29.	J. Asadollahi, K. Khashyarmanesh and Sh. Salarian On the finiteness properties of the generalized local cohomology modules Comm. Algebra 30 (2002), 859-867  [abstract]

30.	K. Khashyarmanesh and Sh. Salarian Asymptotic stability of AttR Tor1R((R/\frakan),A) Proc. Edinburgh Math. Soc. 44 (2001), 479-483  [abstract]

31.	Sh. Salarian, J. Asadollahi and K. Khashyarmanesh Local-Global principle for annihilation of general local cohomology Colloq. Math. 87 (2001), 129-136  [abstract]

32.	K. Khashyarmanesh, Sh. Salarian and H. Zakeri On the associated graded module of ideal generated by an unconditioned strong d-sequence J. Math. Kyoto Univ. 39 (1999), 607-618  [abstract]

33.	K. Khashyarmanesh, Sh. Salarian and H. Zakeri Generalized fractions, determinantal maps and local cohomology modules Ital. J. pure Appl. Math. 6 (1999), 139-146  [abstract]

34.	K. Khashyarmanesh and Sh. Salarian On the associated primes of local cohomology modules Comm. Algebra 27 (1999), 6191-6198  [abstract]

35.	K. Khashyarmanesh, Sh. Salarian and H. Zakeri Characterizations of filter regular sequences and unconditioned strong d-sequences Nagoya Math. J. 151 (1998), 37-50  [abstract]

36.	K. Khashyarmanesh, Sh. Salarian and M. Tousi On the local homology theory for Artinian modules Acta Math. Hungar. 81 (1998), 109-119  [abstract]

37.	K. Khashyarmanesh and Sh. Salarian General local cohomology modules and Koszul homology modules Colloq. Math. 77 (1998), 305-313  [abstract]

38.	K. Khashyarmanesh and Sh. Salarian Filter regular sequences and the finiteness of local cohomology modules Comm. Algebra 26 (1998), 2483-2490  [abstract]

39.	K. Khashyarmanesh, Sh. Salarian and H. Zakeri On the flat dimension of certain modules of generalized fractions Math. J. Toyama Univ. 20 (1997), 79-90  [abstract]

40.	K. Khashyarmanesh and Sh. Salarian Exactness theorem and poor M-Cosequences J. Korean Math. Soc. 34 (1997), 949-957  [abstract]

41.	K. Khashyarmanesh and Sh. Salarian Minimal injective resolutions of modules over Cohen-Macaulay rings Honam Math. J. 19 (1997), 53-59  [abstract]