Shinya Kumashiro

Links to Preprints, In Production, Publications, or Books.

Preprints

1. Traces of semi-invariants (with Ela Celikbas, Jürgen Herzog)
   arXiv:2312.00983, 2023
2. Nearly Gorenstein local rings defined by maximal minors of a 2×n matrix (with Naoyuki Matsuoka, Taiga Nakashima)
   arXiv:2308.04234, 2023
3. On generalized Gorenstein local rings (with Shiro Goto)
   arXiv:2212.12762, 2022
4. Characterization of generalized Gorenstein rings (with Shiro Goto, Ryotaro Isobe, Naoki Taniguchi)
   arXiv:1704.08901, 2017

In Production

Publications

5. The set of trace ideals of curve singularities (with Toshinori Kobayashi)
   Israel Journal of Mathematics, (published online first), 2024
   arXiv:2203.04469, DOI
6. Defining ideals of Cohen-Macaulay fiber cones (with Reza Abdolmaleki)
   International Journal of Algebra and Computation, (published online first), 2024
   arXiv:2405.18041, DOI
7. Reflexive modules over Arf local rings (with Ryotaro Isobe)
   Taiwanese Journal of Mathematics, (published online first), 2024
   arXiv:2105.07184, DOI
8. On a generalized Auslander-Reiten conjecture (with Souvik Dey, Parangama Sarkar)
   Algebras and Representation Theory, 27, 1581-1602, 2024
   arXiv:2209.12718, DOI
9. 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
10. 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
11. When are trace ideals finite?
    Mediterranean Journal of Mathematics, 20, Article number: 278, 2023
    arXiv:2108.00414, DOI, only-view
12. Integrally closed ideals of reduction number three
    Algebra Colloquium, 30, No.2, 315-324, 2023
    arXiv:2105.07186, DOI
13. Graded filtrations and ideals of reduction number 2
    Mathematische Nachrichten, 296, No.5, 1983-1996, 2023
    arXiv:2105.07185, DOI
14. 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
15. 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
16. The reduction number of canonical ideals
    Communications in Algebra, 50, No.11, 4619-4635, 2022
    arXiv:2007.00377, DOI
17. 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
18. 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
19. 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
20. Ideals of reduction number two
    Israel Journal of Mathematics 243, No.1, 45-61, 2021
    arXiv:1911.08918, DOI, only-view
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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