Preprints

35. On embeddings of rings into their canonical modules(with Tran Nguyen An, Mouma Samanta) arXiv:2609.34395, 2026
36. Prescribed initial behavior of μ(I^k)(with Reza Abdolmaleki) arXiv:2606.22933, 2026
37. Modules of minimal multiplicity over one-dimensional Cohen-Macaulay local rings(with Ela Celikbas, Olgur Celikbas, Naoki Endo) arXiv:2510.20170, 2025
38. Canonical traces of graded fiber products: applications to disconnected Stanley–Reisner rings(with Sora Miyashita) arXiv:2506.04899, 2025
39. Full-trace modules(with Ela Celikbas, Olgur Celikbas, Jürgen Herzog) arXiv:2505.14961, 2025
40. Characterization of generalized Gorenstein rings(with Shiro Goto, Ryotaro Isobe, Naoki Taniguchi) arXiv:1704.08901, 2017

In Production

29. On partial trace ideals(with Souvik Dey) Journal of the Mathematical Society of Japan, to appear
    arXiv:2603.10464
30. Traces of semi-invariants(with Ela Celikbas, Jürgen Herzog) Illinois Journal of Mathematics, to appear
    arXiv:2312.00983

Publications

27. The non-pure dual exchange property in low dimensions(with Reza Abdolmaleki) Communications in Algebra, published online, 2026
    arXiv:2606.06949, DOI
28. Characterization of almost Gorenstein rings in terms of the trace ideal(with Ryotaro Isobe) Journal of Algebra and its Applications, published online, 2026
    arXiv:2510.20170, DOI
29. Quasi-factorially closed subalgebras of Laurent polynomial rings (with Takanori Nagamine) Mathematische Nachrichten, published online, 2026
    arXiv:2603.25013, DOI
30. On generalized Gorenstein local rings(with Shiro Goto) Journal of Algebra, 693, 98-156, 2026
    arXiv:2212.12762, DOI
31. Nearly Gorenstein local rings defined by maximal minors of a 2×n matrix(with Naoyuki Matsuoka, Taiga Nakashima) Semigroup Forum, 110, 317-343, 2025 (Open Access)
    arXiv:2308.04234, DOI
32. Defining ideals of Cohen-Macaulay fiber cones(with Reza Abdolmaleki) International Journal of Algebra and Computation, 34(7), 1099-1109, 2024
    arXiv:2405.18041, DOI
33. Reflexive modules over Arf local rings(with Ryotaro Isobe) Taiwanese Journal of Mathematics, 28(5), 865-875, 2024 (Open Access)
    arXiv:2105.07184, DOI
34. The set of trace ideals of curve singularities(with Toshinori Kobayashi) Israel Journal of Mathematics, 265, 153-184, 2025
    arXiv:2203.04469, DOI, only-view
35. On a generalized Auslander-Reiten conjecture(with Souvik Dey, Parangama Sarkar) Algebras and Representation Theory, 27, 1581-1602, 2024
    arXiv:2209.12718, DOI
36. On the sectional genera and Cohen-Macaulay rings(with Hoang Le Truong, Hoang Ngoc Yen) Journal of Commutative Algebra, 15, No.4, 577-594, 2023
    arXiv:2206.04859, DOI
37. The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings Journal of Pure and Applied Algebra, 227, No.11, 107420, 2023
    arXiv:1906.02669, DOI
38. When are trace ideals finite? Mediterranean Journal of Mathematics, 20, Article number: 278, 2023
    arXiv:2108.00414, DOI, only-view
39. Integrally closed ideals of reduction number three Algebra Colloquium, 30, No.2, 315-324, 2023
    arXiv:2105.07186, DOI
40. Graded filtrations and ideals of reduction number 2 Mathematische Nachrichten, 296, No.5, 1983-1996, 2023
    arXiv:2105.07185, DOI
41. The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one(with Jürgen Herzog, Dumitru I. Stamate) Journal of Algebra, 619, 626-642, 2023
    arXiv:2106.09404, DOI
42. The irreducible multiplicity and Ulrich modules(with Tran Nguyen An) Rocky Mountain Journal of Mathematics, 52, No.5, 1795-1799, 2022
    arXiv:2109.00726, DOI
43. The reduction number of canonical ideals Communications in Algebra, 50, No.11, 4619-4635, 2022
    arXiv:2007.00377, DOI
44. Upper bound on the colength of the trace of the canonical module in dimension one(with Jürgen Herzog) Archiv der Mathematik, 119, No.3, 237-246, 2022
    arXiv:2201.12508, DOI, only-view
45. Reducibility index and sum-reducibility index(with Tran Nguyen An, Tran Duc Dung, Le Thanh Nhan) Journal of Algebra and its Applications, 21, No.8, 2250152(13 pages), 2022
    arXiv:2003.03953, DOI
46. Graded Bourbaki ideals of graded modules(with Jürgen Herzog, Dumitru I. Stamate) Mathematische Zeitschrift, 299, No.3-4, 1303-1330, 2021
    arXiv:2002.09596, DOI
47. Ideals of reduction number two Israel Journal of Mathematics 243, No.1, 45-61, 2021
    arXiv:1911.08918, DOI, only-view
48. Certain monomial ideals whose numbers of generators of powers descend(with Reza Abdolmaleki) Archiv der Mathematik, 116, No.6, 637-645, 2021
    arXiv:2005.09991, DOI, only-view
49. Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings(with Shiro Goto, Ryotaro Isobe) Journal of Pure and Applied Algebra, 224, No.2, 747-767, 2020
    arXiv:1802.08409, DOI
50. Residually faithful modules and the Cohen-Macaulay type of idealizations(with Shiro Goto, Nguyen Thi Hong Loan) Journal of the Mathematical Society of Japan, 71, No.4, 1269-1291, 2019
    arXiv:1804.07885, DOI
51. Sally modules of canonical ideals in dimension one and 2-AGL rings(with Tran Do Minh Chau, Shiro Goto, Naoyuki Matsuoka) Journal of Algebra, 521, 299-330, 2019
    arXiv:1704.00997, DOI
52. The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one(with Shiro Goto, Ryotaro Isobe) Acta Mathematica Vietnamica, 44, No.1, 65-82, 2019
    arXiv:1804.06643, DOI, only-view
53. When is R ⋉ I an almost Gorenstein local ring?(with Shiro Goto) Proceedings of the American Mathematical Society, 146, No.4, 1431-1437, 2018
    arXiv:1704.05961, DOI

Books

1. Modern Algebra 2(with Tran Nguyen An, Nguyen Van Hoang) Thai Nguyen University Publishing House, ISBN:978-604-9987-40-3, 2021
   Thai Nguyen University Publishing House