******************* Researchers

Nguyen Tu Cuong
Full Professor, Doctor of Science

Cộng tác viên
Research interests:

Commutative Algebra and Algebraic Geometry

Address
Office: Building A6, Room 410
Tel: +84 4 38361121 /410
Email: ntcuong AT math.ac.vn

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 Tuan Long
  7. Nguyen Thi Dung (2005)
  8. Doan Trung Cuong (2007)
  9. Nguyen Van Hoang (2009)
  10. Tran Nguyen An (2011)
  11. Pham Huu Khanh (2012)
  12. Hoang Le Truong (2013)
  13. Pham Hung Quy

Current Ph.D. students

  1. 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)

Honors

  • Hochiminh Prize in Science and Technology 2016 (shared with Professors Ngo Viet Trung and Le Tuan Hoa)


PUBLICATIONS

List of publications in MathSciNet



List of recent publications
1Nguyen Tu Cuong, Pham Hung Quy, On the structure of finitely generated modules and the unmixed degrees, Journal of Pure and Applied Algebra Volume 229, Issue 7, July 2025, 108000, (SCI-E, Scopus).
2Nguyen Tu Cuong, Nguyen Tuan Long, Hoàng Lê Trường , On Hilbert coefficients and sequentially generalized Cohen-Macaulay modules, Journal of Algebra and Its Applications, 23, No.3 (2024), 2450055 (18 pages), (SCI-E, Scopus).
3Nguyen Tu Cuong, Pham Hung Quy, On the limit closure of a sequence of elements in local rings. Journal of Pure and Applied Algebra 226 (2022), no. 8, Paper No. 107027, 20 pp, (SCI-E, Scopus).
4Nguyen Tu Cuong, Phạm Hùng Quý, On the Index of Reducibility of Parameter Ideals: the Stable and Limit Values, Acta Mathematica Vietnamica, 45(2020), 249–260, Scopus.
5Nguyen Tu Cuong, Pham Hung Quy, Hoàng Lê Trường, The index of reducibility of powers of a standard parameter ideal, Journal of Algebra and Its Applications 18 (2019), 1950048, 17 pp, SCI(-E), Scopus.
6Nguyen Tu Cuong, Doan Trung Cuong, Local Cohomology Annihilators and Macaulayfication, Acta Mathematica Vietnamica, 42 (2017),pp 37–60, (Scopus).
7Nguyen Tu Cuong, Pham Hung Quy, Hoàng Lê Trường, On the index of reducibility in Noetherian modules, Journal of Pure and Applied Algebra, 219 (2015), 4510-4520, SCI(-E), Scopus.
8Nguyen Tu Cuong, Nguyen Tuan Long, Hoàng Lê Trường, Uniform bounds in sequentially generalized Cohen-Macaulay modules, Vietnam Journal of Mathematics, 45 (2015), 343-356, Scopus.
9Nguyen Tu Cuong, S. Goto, N.V. Hoàng, On the cofiniteness of generalized local cohomologymodules, Kyoto Journal of Mathematics, 55 (2015), 169-185, SCI(-E), Scopus.
10Nguyen Tu Cuong, Nguyen Van Hoang, On the finiteness and stability of certain sets of associated prime ideals of local cohomology modules. Communications in Algebra 42 (2014), 1757–1768, SCI(-E); Scopus.
11Nguyen Tu Cuong, Hoàng Lê Trường, Shiro Goto, Hillbert coefficients and sequentially Cohen-Macaulay modules, Journal of Pure and Applied Algebra 217 (2013), 470–480, SCI(-E); Scopus.
12Nguyen Tu Cuong, Hoàng Lê Trường, Shiro Goto, The equality $I^2 =qI$  in sequentially Cohen-Macaulay rings,  Journal of Algebra, 379 (2013), 50 - 79, SCI(-E); Scopus.
13Nguyen 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, SCI(-E); Scopus.
14Nguyen Tu Cuong, P. H. Khanh, On some asymptotic properties of finitely generated modules, Acta Mathematica Vietnamica 36 (2011), 183 -- 192, Scopus.
15Nguyen 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, SCI(-E); Scopus.
16Nguyen Tu Cuong, Doan Trung Cuong, Hoàng Lê Trường, 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, SCI(-E); Scopus.
17Nguyen 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.
18Hoàng Lê Trường, Nguyen Tu Cuong, Parametric decomposition of parameter ideals and sequentially Cohen-Macaulay modules, Proc. Amer. Math. Soc., 137 (2009), 19-26.
19Hoàng Lê Trường, Nguyen Tu Cuong, Asymptotic behavior of parameter ideals in generalized Cohen-Macaulay modules, J. Algebra 320 (2008),  158 - 168.
20Nguyen 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.
21Nguyen Tu Cuong, T. T. Nam, A local homology theory for linearly compact modules, J. Algebra 319 (2008),4712 - 4737 preprint arXiv:0709.1778.
22Nguyen Tu Cuong, Doan Trung Cuong, On sequentially Cohen-Macaulay modules, Kodai Math. J. 30 (2007),  409 - 428, preprint arXiv:math/0507202.
23Nguyen Tu Cuong, N. T. Dung and L. T. Nhan, Generalized co-Cohen-Macaulay and co-Buchsbaum modules, Algebra Colloq. 14 (2007), 265 – 278.
24Nguyen 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.
25Nguyen 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.
26Nguyen Tu Cuong, Doan Trung Cuong, On the structure of sequentially generalized Cohen-Macaulay modules, J. Algebra 317 (2007),  714 - 742, preprint arXiv:math/0701729.
27Nguyen Tu Cuong, Nguyen Thi Hong Loan, A blowing-up characterization of pseudo Buchsbaum modules, Vietnam J. Math. 34 (2006), 449 - 458.
28Nguyen Tu Cuong, N. V. Hoang, Some finite properties of generalized local cohomology modules, East-West J. Math. 7 (2005), 107 - 115.
29Nguyen Tu Cuong, N. T. H. Loan, A characterization for pseudo Buchsbaum modules. Japan. J. Math. (N.S.), 30 (2004), 165 - 181.
30Nguyen 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.
31Nguyen Tu Cuong, Lectures on modern algebra (in Vietnamese) - Giáo trình đại số hiện đại. NXB Đại học Quốc gia, Hà Nội, 2003, 183 trang.
32Nguyen Tu Cuong, Le Thanh Nhan, Pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay modules, J. Algebra 267 (2003), 156 - 177.
33Nguyen Tu Cuong, M. Morales and L. T. Nhan, On the length of generalized fractions, J. Algebra 265 (2003), 100 - 113.
34Nguyen Tu Cuong, Doan Trung Cuong, dd-sequences and partial Euler-Poincaré characteristics of Koszul complex, Vietnam J. Math. 31 (2003), N0 3, 353 - 358.
35Nguyen Tu Cuong, Nguyen Thai Hoa, Parametrical Characterizations for Pseudo and Sequentially Cohen-Macaulay Modules, Vietnam Journal of Mathematics, 30 (2002), 417-420.
36Nguyen Tu Cuong, Le Thanh Nhan, On the Noetherian dimension of Artinian modules, Vietnam J. Math. 30 (2002), 121 - 130.
37Nguyen Tu Cuong, Nguyen Thi Hong Loan, On pseudo-Buchsbaum modules, Vietnam J. Math. 30 (2002), 299 - 303.
38Nguyen Tu Cuong, Le Thanh Nhan, On representable linearly compact modules, Proc. Amer. Math. Soc. 130 (2002), 1927 - 1936 (electronic).
39Nguyen 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.
40Nguyen 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.
41Nguyen Tu Cuong, Tran Tuan Nam, The I-adic completion and local homology for Artinian modules. Math. Proc. Cambridge Philos. Soc. 131 (2001), 61 - 72.
42Nguyen Tu Cuong, Nguyen Duc Minh, Length of generalized fractions of modules having small polynomial type. Math. Proc. Cambridge Philos. Soc. 128 (2000), 269 - 282.
43Nguyen Tu Cuong, Le Thanh Nhan, On representable linearly compact modules, Vietnam J. Math. 28 (2000), 291 - 294.
44Nguyen Tu Cuong, Tran Tuan Nam, Local homology modules for linearly compact modules. Vietnam J. Math. 28 (2000), 87 - 91.
45Nguyen 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.
46Nguyen Tu Cuong, L. T. Nhan, Dimension, multiplicity and Hilbert function of Artin modules. East-West J. Math. 2 (1999), 179 - 196.
47Nguyen 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.
48Nguyen Tu Cuong, Remarks on the non-Cohen-Macaulay locus of Noetherian schemes. Proc. Amer. Math. Soc. 126 (1998), 1017 - 1022.
49Nguyen Tu Cuong, Nguyen Duc Minh, On the length of generalized fractions of modules having polynomial type <= 2. Vietnam J. Math. 26 (1998), 87 - 90.
50Nguyen 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.
51Nguyen Tu Cuong, Nguyen Duc Minh, On the lengths of Koszul homology modules and generalized fractions. Math. Proc. Cambridge Philos. Soc. 120 (1996), 31 - 42.
52Nguyen 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.
53Nguyen Tu Cuong, P-standard systems of parameters and p-standard ideals in local rings. Acta Math. Vienam. 20 (1995), N0 1, 146 - 161.
54Nguyen 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.
55Nguyen 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.
56Nguyen 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.
57Nguyen Tu Cuong, On the length of the powers of a system of parameters in local rings. Nagoya Math. J. 120 (1990), 77 - 88.
58Nguyen Tu Cuong, Trivialite des deploiements de reseaux holomoes. Bull. Math. France Memoire 6 (1981), 78 - 85.
59Nguyen Tu Cuong, Ngo Viet Trung, Uber schwache Sequenzen. Period. Math. Hungar. 11 (1981), 77 - 80.
60Nguyen Tu Cuong, Freie Auflosung eines flachen holonomen Systems und ihre Entfaltungen. Seminar-berichte Humboldt Univ. 39 (1981), 1 - 41.
61Ha Huy Vui, Nguyen Tu Cuong, Nguyễn Sĩ Minh, Nguyễn Hữu Đức, A rostkax beskonechnoi opredelenosti. Acta Math. Vietmam. 3 (1978), 43 - 50.
62Peter Schenzel, Ngo Viet Trung, Nguyen Tu Cuong, Uber verallgemeinerte Cohen- Macaulay Moduln. Math. Nachr. 85 (1978),  57 - 73.
63Ha 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.