Professor at Kharazmi University, IRAN
Commutative Algebra
Retired, March 2018
Faculty of Mathematics and Computer Sciences , Kharazmi University,
50 Taleghani Ave., P.O. Box 15618-36314, Tehran, Iran.
Institute for Studies in Theoretical Physics and Mathematics (IPM),
P.O. Box 19394-5746, Tehran, Iran; IPM homepage.
Education:
BSc, Ferdowsi University of Mashhad, 1966-1969 (1345-1348).
MSc, Kharazmi University (KU) 1970-1971 (1349-1350) & Oxford University 1974-1975 (1353-1354).
PhD, KU, 1994-1998 (1370-1373). Advisor: Hossein Zakeri; Thesis title: The structure of dualizing complexes for rings which are (S_2).
Employment:
Assistant Professor at KU, 1972-2002.
Associate Professor at KU, 2002-2006.
Professor at KU, 2007.
Activities: Coauthor of the following general math. educational books:
Mathematics, for the third year of Iranian Secondary Schools, 1987;
Mathematics, for the second year of Iranian Secondary Schools, 1986;
Mathematics, for the first year of Iranian Secondary Schools, 1986;
Mathematics, for the fifth year of Iranian Elementary Schools, 1985;
Mathematics, for the second year of Iranian Elementary Schools, 1984.
Research Topics:
My main interests lie in commutative algebra. The basic object I study is a commutative Noetherian ring R. Some of the topics I have worked on concern local cohomology, homological problems, Cohen-Macaulay and Gorenstein rings, complexes of modules of generalized fractions, dualizing complexes, Cousin complexes, the derived category, linkage of modules.
Teaching
BSc. : Group Theory, Linear Algebra, Galois Theory, Elementary Number Theory, Calculus.
MSc. : Homological Algebra 1, Commutative Algebra 1.
PhD. : Homological Algebra 2 and 3, Commutative Algebra 2 and 3, Complexes in Commutative Algebra ( spectral sequences, Cousin complexes, complexes of modules of generalized fractions, and dualizing complexes}).
Experiences
(1998 -- ... ) Researcher at the Institute for Studies in Theoretical Physics and Mathematics(IPM), Tehran.
(2002-- 2005 ) Researcher at the Mosaheb Institute of Mathematics (MIM), Tehran.
(2017-- ....) Editor of Bulletin of the Iranian Mathematical Society (BIMS).
(2020 -- 2022) Algebra Section Editor of BIMS.
(2020-2022) Director of the Commutative Algebra Group of the IPM.
Alireza Nazari (2008),
thesis title: Local Cohomology and Regularity over Standard Graded Rings.
Alireza Vahidi-Sepidan (2009),
thesis title: Extension, Torsion and Section Functors of Local cohomology Modules.
Raheleh Jafari (2011),
thesis title: Cousin complexes and applications.
Mohsen Gheibi (2013),
thesis title: Linkage of Modules, Exact Zero-Divisors and their Applications.
Arash Sadeghi (2013),
thesis title: Linkage of Finite Gorenstein Dimension Modules.
Ensiyeh Amanzadeh (2015),
thesis title: Semidualizing Modules and Related Classes.
Mehran Rahimy (2020),
thesis title: Properties of Almost Gorenstein Rings.
Mohammad Eghbali (2020),
thesis title: Study of Modules over Rings of Prime Characteristics.
Yaser Khalatpour (2021),
thesis title: Some Applications of Delta Invariant and Linkage Theory.
Speaker at:
2004, The Second Commutative Algebra Seminar and related Topics, IPM, Iran.
2004, Mini Workshop on Commutative Algebra, University of Duisburg-Essen, Germany.
2005, The 16th Iranian Algebra Seminar, Zanjan.
2006, CIMPA School and International Conference on Commutative Algebra, Vietnam.
2007, Homological and Combinatorial Aspects in Commutative Algebra , Bustini, Romania.
2008, Homological and Combinatorial Aspects in Commutative Algebra, Fez, Morocco.
2008, The CIMPA school and international conference on commutative algebra, IIT, India.
2009, INSPAM, Mathematics Department, Universiti Putra Malaysia, Malaysia.
2010, The CIMPA school and international conference on commutative algebra, Istanbul, Turkey.
2011, The 8th Commutative Algebra Seminar and related Topics, IPM, Iran.
2016, The International Conference and 8th Japan-Vietnam joint Seminar on Commutative Algebra, Ha Long, Vietnam.
2016, The Second International Workshop and Conference on Commutative Algebra, Tribhuvan University, Kathmandu, Nepal.
F. Dehghani-Zadeh, --- and A. Sadeghi, Linkage of modules by reflexive morphisms, Journal of the Mathematical Society of Japan, Vol. 74, No. 1 (2022), 25-77.
--- and Y. Khalatpour, A study of strongly Cohen–Macaulay ideals by delta invariant, Bulletin of the Iranian Mathematical Society 46 (2020), 1659-1667.
--- , M. Eghbali and Y. Khalatpour, On the interplay between the Frobenius functor and its dual, Journal of Algebra and Its Applications, DOI:10.1142/S0219498821500894.
--- and A. Sadeghi, Linkage of modules with respect to a semidualizing module, Pacific Journal Math., 294 (2018), 307--328.
O. Celikbas, ---, M. Gheibi, A. Sadeghi and R. Takahashi, Associated primes and syzygies of modules, J. Commut. Algebra 11(2019), 301-323.
E. Amanzadeh and ---, Presentations of rings with a chain of semidualizing modules, Mathematica Scandinavica, 121 (2017), 161--185.
E. Amanzadeh and ---, Complexes of $C$-projective modules, Bull. Iranian Math. Soc. 42 (2016), 949-958.
--- and A. Sadeghi, Linkage of modules and the Serre conditions, Journal of Pure and Applied Algebra, 219 (2015), 4458-4478.
E. Amanzadeh and ---, Auslander class, $\G_C$-and $C$-projective modules modulo exact zero-divisors, Communications in Algebra, 43 (2015), 4320-4333.
--- and A. Sadeghi, Linkage of finite Gorenstein dimension modules, Journal of Algebra, 376 (2013), 261-278.
---, M. Gheibi, S. H. Hassanzadeh, and A. Sadeghi, Linkage of modules over Cohen-Macaulay rings, Journal of Algebra, 335 (2011), 177-187.
--- and R. Jafari, Cohen-Macaulay loci of modules, Communications in Algebra, 39 (2011), 3681-3697.
--- and A. Vahidi. Torsion functors of local cohomology modules, Algebra Representation Theory, 14 (2011), 79-85.
--- and A. Vahidi, Non-Artinian local cohomology modules, Canadian Mathematical Bulletin, 54 (2011), 619-629.
--- and R. Jafari, Modules with finite Cousin complexes have uniform local cohomological annihilators, Journal of Algebra, 319 (2008), 3291-3300.
--- and S. Yassemi, Bass numbers of local cohomology modules with respect to an ideal, Algebra Representation Theory, 11(2008), 299-306.
--- and R. Jafari, Top local cohomology modules with specified attached primes, Algebra Colloquium, 15 (2008), 341-344.
--- and A. Nazari, Graded local cohomology: attached and associated primes, asymptotic behaviors, Communications in Algebra, 35 (2007), 1567-1576.
--- and S. Yassemi, Some rigidity results for highest order local cohomology modules, Algebra Colloquium, 14 (2007), 497-504.
--- and S. Yassemi, Top local cohomology modules, Algebra Colloquium, 14 (2007), 209-214.
--- and S. Yassemi, Finiteness of extension functors of local cohomology module, Communications in Algebra, 34 (2006), 3097--3101.
--- and S. Yassemi, Associated primes of the local cohomology modules, "Abelian Groups, Rings, and Modules", published in honor of Edgar Enochs in the book series "Lecture Note in Pure and Applied Mathematics" by Taylor & Francis, 2006.
--- and S. Yassemi, Associated primes and cofiniteness of local cohomology modules, manuscripta mathematica, 117 (2005), 199-205.
--- and S. Yassemi, Attached primes of the top local cohomology modules with respect to an ideal, Arch. Math., 84(2005), 292-297.
---, A study of Cousin complexes through the dualizing complexes, Communications in Algebra, 33 (2005), 119-132.
--- and S. Yassemi, Generalized local cohomology and the Intersection Theorem, Communications in Algebra, 33 (2005), 899-908.
--- and S. Yassemi, Cohomological dimension of complexes, Communications in Algebra, 32 (2004), 4375-4386.
--- and M. Tousi, A generalization of the dualizing complex structure and its applications, J. Pure Appl. Algebra 155 (2001), 17--28.
--- and M. Tousi, The structure of dualizing complex for a ring which is (S_2), J. Math. Kyoto Univ., 38(1998), 503--516.
Updated: January 26, 2022.