Nguyen Tu Cuong


Full Professor, Doctor of Science

Department of Algebra
Research interests:

Commutative Algebra and Algebraic Geometry


Address
Office: Building A6, Room 410
Tel: +84 4 37563474 /410
Email: ntcuong AT math.ac.vn
Personal homepage: http://vie.math.ac.vn/~ntcuong/

Education

  • Dr. Sc.: 1995, Institute of Mathematics, Hanoi, Vietnam
  • Ph. D.: 1982, Humboldt University Berlin, Germany
  • M. Sc.: 1969, Martin-Luther University, Halle, Germany



 Ph.D. students

Graduated Ph.D. students

  1. Nguyen Duc Minh (1995)
  2. Tran Tuan Nam (2001)
  3. Le Thanh Nhan (2001)
  4. Nguyen Thai Hoa (2003)
  5. Nguyen Thi Hong Loan (2004)
  6. Nguyen Thi Dung (2005)
  7. Doan Trung Cuong (2007)
  8. Nguyen Van Hoang (2009)
  9. Tran Nguyen An (2011)
  10. Pham Huu Khanh (2012)
  11. Hoang Le Truong (2013)
  12. Pham Hung Quy

Current Ph.D. students

  1. Nguyen Tuan Long
  2. Tran Duc Dung


Editorship


  •  Acta Mathematica Vietnamica (Editor-in-Chief, 2007-present)
  •  East-West Journal of Mathematics (Founding editor, 1998-present)
  •  Vietnam Journal of Mathematics (1995-2007)


PUBLICATIONS

List of publications in MathSciNet



List of recent publications
1Nguyen Tu Cuong, Doan Trung Cuong, Local Cohomology Annihilators and Macaulayfication, Acta Mathematica Vietnamica, 42 (2017),pp 37–60.
2Nguyen Tu Cuong, Pham Hung Quy, Hoang Le Truong, On the index of reducibility in Noetherian modules, Journal of Pure and Applied Algebra, 219 (2015), 4510-4520.
3Nguyen Tu Cuong, Nguyen Tuan Long, Hoang Le Truong, Uniform bounds in sequentially generalized Cohen-Macaulay modules, Vietnam Journal of Mathematics, 45 (2015), 343-356.
4Nguyen Tu Cuong, S. Goto, N.V. Hoàng, On the cofiniteness of generalized local cohomologymodules, Kyoto Journal of Mathematics, 55 (2015), 169-185.
5Nguyen Tu Cuong, Nguyen Van Hoang, On the finiteness and stability of certain sets of associated prime ideals of local cohomology modules. Comm. Algebra 42 (2014), 1757–1768.
6Nguyen Tu Cuong, Hoang Le Truong, Shiro Goto, Hillbert coefficients and sequentially Cohen-Macaulay modules, Journal of Pure and Applied Algebra 217 (2013), 470–480preprint arXiv:1206.5879.
7Nguyen Tu Cuong, Hoang Le Truong, Shiro Goto, The equality $I^2 =qI$  in sequentially Cohen-Macaulay rings,  Journal of Algebra, 379 (2013), 50 - 79.
8Nguyen Tu Cuong, P. H. Quy, A splitting theorem for local cohomology and its applications,  Journal of Algebra  331 (2011), 512 -- 522. preprint  arXiv:1009.3531.
9Nguyen Tu Cuong, P. H. Khanh, On some asymptotic properties of finitely generated modulesActa Math. Vietnamica  36 (2011), 183 -- 192.
10Nguyen Tu Cuong, N. V. Hoang and P. H. Khanh, Asymptotic stability of certain sets of associated prime ideals if local cohomology modules,  Communications in Algebra  38 (2010), 4416 -- 4429.
11Nguyen Tu Cuong, Doan Trung Cuong, Hoang Le Truong, On a new invariant of finitely generated modules over local rings,  Journal of Algebra and its Applications  9 (2010), 959 -- 976, preprint   arXiv:1003.3972.
12Nguyen Tu Cuong, L. T. Nhan and N. T. K. Nga, On pseudo supports and non-Cohen-Macaulay locus of finitely generated modules,  J. Algebra,323 (2010), 3029 -- 3038.
13Nguyen Tu Cuong, Hoang Le Truong, Parametric decomposition of parameter ideals and sequentially Cohen-Macaulay modules, Proc. Amer. Math. Soc., 137 (2009), 19-26.
14Nguyen Tu Cuong, Hoang Le Truong, Asymptotic behavior of parameter ideals in generalized Cohen-Macaulay modules, J. Algebra 320 (2008),  158 - 168.
15Nguyen Tu Cuong, N. V. Hoang, On the vanishing and the finiteness of supports of generalized local cohomology modules, Manuscripta Math. 126 (2008), 59 - 72, preprint arXiv:0705.4553.
16Nguyen Tu Cuong, T. T. Nam, A local homology theory for linearly compact modules, J. Algebra 319 (2008),4712 - 4737 preprint arXiv:0709.1778.
17Nguyen Tu Cuong, Doan Trung Cuong, On sequentially Cohen-Macaulay modules, Kodai Math. J. 30 (2007),  409 - 428, preprint arXiv:math/0507202.
18Nguyen Tu Cuong, N. T. Dung and L. T. Nhan, Generalized co-Cohen-Macaulay and co-Buchsbaum modules, Algebra Colloq. 14 (2007), 265 – 278.
19Nguyen Tu Cuong, Doan Trung Cuong, dd-sequences and partial Euler-Poincare characteristics of Koszul complex. J. Algebra Appl. 6 (2007),  207 - 231, preprint arXiv:math/0507200.
20Nguyen Tu Cuong, N. T. Dung; L. T. Nhan, Top local cohomology and the catenaricity of the unmixed support of a finitely generated module, Comm. Algebra 35 (2007),  1691 - 1701, preprint arXiv:math/0701675.
21Nguyen Tu Cuong, Doan Trung Cuong, On the structure of sequentially generalized Cohen-Macaulay modules, J. Algebra 317 (2007),  714 - 742, preprint arXiv:math/0701729.
22Nguyen Tu Cuong, Nguyen Thi Hong Loan, A blowing-up characterization of pseudo Buchsbaum modules, Vietnam J. Math. 34 (2006), 449 - 458.
23Nguyen Tu Cuong, N. V. Hoang, Some finite properties of generalized local cohomology modules, East-West J. Math. 7 (2005), 107 - 115.
24Nguyen Tu Cuong, N. T. H. Loan, A characterization for pseudo Buchsbaum modules. Japan. J. Math. (N.S.), 30 (2004), 165 - 181.
25Nguyen Tu Cuong, M. Morales and L. T. Nhan, The finiteness of certain sets of attached prime ideals and the length of generalized fractions, J. Pure Appl. Algebra 189 (2004), 109 - 121.
26Nguyen Tu Cuong, Lectures on modern algebra (in Vietnamese) - Giáo trình đại số hiện đại. NXB Đại học Quốc gia, Hà Nội, 2003, 183 trang.
27Nguyen Tu Cuong, Le Thanh Nhan, Pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay modules, J. Algebra 267 (2003), 156 - 177.
28Nguyen Tu Cuong, M. Morales and L. T. Nhan, On the length of generalized fractions, J. Algebra 265 (2003), 100 - 113.
29Nguyen Tu Cuong, Doan Trung Cuong, dd-sequences and partial Euler-Poincaré characteristics of Koszul complex, Vietnam J. Math. 31 (2003), N0 3, 353 - 358.
30Nguyen Tu Cuong, Nguyen Thai Hoa, Parametrical Characterizations for Pseudo and Sequentially Cohen-Macaulay Modules, Vietnam Journal of Mathematics, 30 (2002), 417-420.
31Nguyen Tu Cuong, Le Thanh Nhan, On the Noetherian dimension of Artinian modules, Vietnam J. Math. 30 (2002), 121 - 130.
32Nguyen Tu Cuong, Nguyen Thi Hong Loan, On pseudo-Buchsbaum modules, Vietnam J. Math. 30 (2002), 299 - 303.
33Nguyen Tu Cuong, Le Thanh Nhan, On representable linearly compact modulesProc. Amer. Math. Soc. 130 (2002), 1927 - 1936 (electronic).
34Nguyen Tu Cuong, Tran Tuan Nam, On the co-localization, co-support and co-associated primes of local homology modules. Vietnam J. Math. 29 (2001), N0 4, 359 - 368.
35Nguyen Tu Cuong, N. T. Hoa and L. T. Nhan, On modules whose local cohomology modules have generalized Cohen-Macaulay Matlis duals. East-West J. Math. 3 (2001), 109 - 123.
36Nguyen Tu Cuong, Tran Tuan Nam, The I-adic completion and local homology for Artinian modules. Math. Proc. Cambridge Philos. Soc. 131 (2001), 61 - 72.
37Nguyen Tu Cuong, Nguyen Duc Minh, Length of generalized fractions of modules having small polynomial type. Math. Proc. Cambridge Philos. Soc. 128 (2000), 269 - 282.
38Nguyen Tu Cuong, Le Thanh Nhan, On representable linearly compact modules, Vietnam J. Math. 28 (2000), 291 - 294.
39Nguyen Tu Cuong, Tran Tuan Nam, Local homology modules for linearly compact modules. Vietnam J. Math. 28 (2000), 87 - 91.
40Nguyen Tu Cuong, Vu The Khoi, Modules whose local cohomology modules have Cohen-Macaulay Matlis duals. In: Proceedings of Hanoi Conf. on Commutative Algebra Algebra Geometry and Computational Methods, Editor by D. Eisenbud, Springer Verlag, 1999, 223 - 232.
41Nguyen Tu Cuong, L. T. Nhan, Dimension, multiplicity and Hilbert function of Artin modules. East-West J. Math. 2 (1999), 179 - 196.
42Nguyen Tu Cuong, Nguyen Thai Hoa, and Nguyen Thi Hong Loan, On certain length functions associated to a system of parameters in local rings. Vietnam J. Math. 27 (1999), 259 - 272.
43Nguyen Tu Cuong, Remarks on the non-Cohen-Macaulay locus of Noetherian schemes. Proc. Amer. Math. Soc. 126 (1998), 1017 - 1022.
44Nguyen Tu Cuong, Nguyen Duc Minh, On the length of generalized fractions of modules having polynomial type <= 2. Vietnam J. Math. 26 (1998), 87 - 90.
45Nguyen Tu Cuong, Vu The Khoi, A lower bound for index of reducibility of parameter ideals in local rings. Vietnam J. Math. 25 (1997), 341 - 347.
46Nguyen Tu Cuong, Nguyen Duc Minh, On the lengths of Koszul homology modules and generalized fractions. Math. Proc. Cambridge Philos. Soc. 120 (1996), 31 - 42.
47Nguyen Tu Cuong, Vu The Khoi, On the partial Euler-Poincare characteristic of certain systems of parameters in local rings. Math. Z. 222 (1996), 383 - 390.
48Nguyen Tu Cuong, P-standard systems of parameters and p-standard ideals in local rings. Acta Math. Vienam. 20 (1995), N0 1, 146 - 161.
49Nguyen Tu Cuong, On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings. Nagoya Math. J. 125 (1992), 105 - 114.
50Nguyen Tu Cuong, Nguyen Duc Minh, Openness of locus of points having polynomial types bounded above by a constant. Vietnam J. Math. 20 (1992), 71 - 76.
51Nguyen Tu Cuong, On the dimension of the non-Cohen-Macaulay locus of local rings admitting dualizing complexes. Math. Proc. Cambridge Philos. Soc. 109 (1991), 479 - 488.
52Nguyen Tu Cuong, On the length of the powers of a system of parameters in local rings. Nagoya Math. J. 120 (1990), 77 - 88.
53Nguyen Tu Cuong, Trivialite des deploiements de reseaux holomoes. Bull. Math. France Memoire 6 (1981), 78 - 85.
54Nguyen Tu Cuong, Ngo Viet Trung, Uber schwache Sequenzen. Period. Math. Hungar. 11 (1981), 77 - 80.
55Nguyen Tu Cuong, Freie Auflosung eines flachen holonomen Systems und ihre Entfaltungen. Seminar-berichte Humboldt Univ. 39 (1981), 1 - 41.
56Ha Huy Vui, Nguyen Tu Cuong, Nguyễn Sĩ Minh, Nguyễn Hữu Đức, A rostkax beskonechnoi opredelenosti. Acta Math. Vietmam. 3 (1978), 43 - 50.
57Peter Schenzel, Ngo Viet Trung, Nguyen Tu Cuong, Uber verallgemeinerte Cohen- Macaulay Moduln. Math. Nachr. 85 (1978),  57 - 73.
58Ha Huy Vui, Nguyen Tu Cuong, N. H. Duc, N. S. Minh, Sur les germes de functions infiniment determines. C. R. Acad. Sc. Paris 285 (1977), 1045 - 1048.