自我简介  1992.2-1994.6在南京大学数学系攻读博士学位, 并于1995年初获博士学位。1995.9-1997.2在复旦大学数学研究所做博士后研究。1997年3月开始在上海交通大学数学系任教，2000年1月任教授，次年1月具备博士生导师资格。2001-2002学年在Harvard大学数学系访问(教育部与Harvard大学联合资助项目)。 主讲的课程包括了本科生的“线性代数”、“概率与统计”、“高等代数与解析几何”、“应用近世代数”（含交大致远学院的线性代数、抽象代数）；研究生的“图与网络”、“抽象代数”、“基础代数学”、 “交换代数与同调代数”、 “环与模范畴”、“同调代数”、“代数K－理论” 等课程。

  主持（完成）三项国家自然科学基金项目、主持（完成）三项省部级项目，为主参加一项国家自然科学基金项目、两项上海市自然科学基金项目。从2005年以来培养博士、硕士多名；在国内外重要刊物上独立或合作发表论文七十余篇（其中含SCI源期刊58篇），其中有多篇被他人多次引用。在攻读博士和做博士后阶段主要研究环的稳定性条件、K_0群的计算和描述；近期研究交换半群与交换环的的组合性质、有限交换局部环的分类与表达；目前的主要兴趣在于组合交换代数。主导的研究群体所获成果在国内外均有一定的影响。

 

目前研究兴趣:  1. 组合交换代数      2.环论与同调代数


Preprints 预印本

 

 

 

● A-Ming Liu, J. Guo and Tongsuo Wu. The Cohen-Macaulay Property of $f$-ideals. Preprint   2020.

 

● S. Yasmeen and Wu Tongsuo.   Grobner basis of  r-star complexes. Comm.  Algebra  Preprint 2019. PP24.

 

● A-M Liu and Wu Tongsuo.  Regularity of house-free graphs and n-gap-free graphs. Preprint. 2019.

 

● J.Guo, Tongsuo Wu and H.Y. Li. Minimum balanced bipartitions of f-graphs. Preprint  PP9.

 

● A-M Liu and Wu Tongsuo. Minimal free resolution of a graded ideal with linear quotients.  Preprint PP4. arXiv: 1610.00055.

 

● Chen L. and Wu Tongsuo. The homology groups of simplicial complexes of zero-divisor graphs.     Preprint. PP8

● Yifan Ren and Wu Tongsuo. Remarks on two theorems in linear algebra. PP5.  Preprint  2019.  arXiv:1911.07130   

 

Refereed Published Paper

 

79. S. Yasmeen and Wu Tongsuo.   Vertex decomposable property of graphs whose complements are r-partite. J. Math. Res. with  Appl.  Preprint 2019.  PP10. [ISSN 2095-2651]

 

78. Wu Tongsuo.  Boolean graphs—A survey.   Proceeding of Eighth CJK Symposium On Rings and Modules.  World Scientific Publishing 2021. 133-147.

 

77.Liu Q.,  Wu T.S. and Guo J.  On finite local rings with clique number four.  Algebra Colloq.   PP21 (accepted)  (SCI)

 

76.  Liu Q.,  Wu T.S. and Guo J.  Finite rings whose graphs have clique number less than five. Algebra Colloq.   PP10 (accepted)   (SCI)

 

75. Liu A-M and Wu Tongsuo.  A construction of  sequentially Cohen-Macaulay graphs.   Algebra Colloq.   

      28: ？ (2021)  (SCI)  PP20. ( Preprint 2018) (SCI)

 

74.D.C. Lu and Wu Tongsuo.  On reduction number of products of ideals. Bull. Iranian Math. Soc.  46(2020) 1027–1033 .   https://doi.org/10.1007/S41980-019-00308-1   (SCI)

 

73. Liu  A-M and Wu Tongsuo.  Edge ideal with regularity no more than three. Algebra Colloq. 27:  4(2020)  761-766.（DOI: 10.1142/S1005386720000644,  to appear） (SCI)

 

72. Guo J. ，Shen Y.H. and Wu Tongsuo.   Strongly shellable simplicial complexes. J. Korean Math. Soc.  56:6(2019) 1613-1639. [Published online November 1, 2019,https://doi.org/10.4134/JKMS.j180831. See also arXiv:1604.05412]  (SCI)

 

71. Liu  A-M and Wu Tongsuo. Boolean graphs are Cohen-Macaulay. Comm. Algebra 46:10(2018)4498-4510.  (A limited 50 copies of free e-prints at   https://www.tandfonline.com/eprint/fTdxnekNTnHRkdID3K53/full ) Preprint .  [arXiv: 1611.07574.  DOI:  10.1080/00927872.2018.1448839.] (SCI)

 

70. S. Yasmeen and Wu Tongsuo. On graded Betti number of a class of graphs. Algebra Colloq. 25:2 (2018) 335–348.  [DOI: 10.1142/S1005386718000238     (preprints)] (SCI)

 

69.  Guo J. ，Shen Y.H. and Wu Tongsuo.   Edgewise strongly shellable clutters.   J.  Algebra  Appl. 17:11 (2018) 1850018 (19 pages) .  [DOI: 10.1142/S0219498818500184   arXiv:1604.05414.] (SCI)

 

68. Guo J., Wu Tongsuo and Yu H.Y.  On rings whose annihilating-ideal graphs are blow-ups of a Boolean graph.  J. Korean Math. Soc.  54 :3(2017)  847–865. [Preprint.] (SCI)

 

67. Guo J., Wu Tongsuo and Liu Q.   F-ideals and f-graphs.  Comm. Algebra 45:8(2017) 3207-3220.  [A limited 50 copies of free e-prints at  http://www.tandfonline.com/eprint/ssgxyIVRBTGud3gvRJS7/full      Preprint]  (SCI)

 

66. T. Aleksandr, Wu Tongsuo and Artem Lopatin. On the lattices of multiply composition formations of finite groups. Bull. Int. Math. Virtual Inst.  6  (2016),  no. 2, 219–226. [Preprint] .

 

65.  Guo J. and Wu  Tongsuo. Graph properties and stratified presentations of partially ordered sets.  Algebra Colloq. 23:1(2016) 51-63 .  (SCI)

 

64. Guo J. and  Wu Tongsuo. Monomial ideals under ideal operations. Comm. Algebra 43:11       (2015)  4745-4762 .  (A limited 50 copies of free e-prints at   https://www.tandfonline.com/eprint/KIRCZVTSnS5a4R4V7w9X/full ) [DOI:  10.1080/00927872.2014.952012. online: 21 Jul 2015]    (SCI)

 

63. Huang CL and  Wu Tongsuo. Ding projective and  Ding injective dimensions.  Intern. Electronic J. Algebra.  18(2015) 1-20.  online: July 9,2015

 

62. Guo J. and Wu Tongsuo.   On the  (n, d)^{th} f-ideals. J. Korean Math. Soc. 52:4(2015) 685-697. (SCI)

 

61. Guo J., Wu Tongsuo and Ye M.  Complemented graphs and blow-ups of Boolean graphs,  with  applications to co-maximal ideal graphs. Filomat   29:4 (2015), 897-908. [ISSN: 0354-5180]  (SCI)

 

60. Yu H.Y. and Wu Tongsuo. Commutative rings R whose C(AG(R)) consists only of triangles.  Comm. Algebra 43:3(2015)   1076-1097   （A limited 50 copies of free e-prints at   https://www.tandfonline.com/eprint/7r4ZHXHStQqiGGQZ6sEQ/full ）DOI:  10.1080/00927872.2013.847950    (SCI)

 

59. Ye. M.，Wu  Tongsuo，Liu Q. and Guo J.  Graph blow-up and its applications in co-maximal ideal graphs.  J.  Algebra  Appl.  14:3(2015)  1550027 (13 pages)      (SCI)

 

 

58. Yu H.Y.，Wu Tongsuo and  Gu W.P.  Artinian local rings whose annihilating-ideal graphs are star graphs. Algebra Colloq. 22:1 (2015) 73-82   DOI: 10.1142/S1005386715000073  (SCI)

 

57. 郭锦、武同锁.    Lyubeznik分解为极小自由分解的单项式理想 （in Chinese），西南大学学报 36:10（2014）95-97.

 

56. Wu Tongsuo,  Li Y.L. and Lu D.C. Zero divisors and prime elements of bounded semirings.  Front. Math. China  9:6(2014) 1381-1399. (DOI) 10.1007/s11464-014-0423-1 (Published online 2014.09.07)  (SCI)   

 

55. Ye M., Wu Tongsuo, Liu Q. and Yu H. Implements of graph blow-up in co-maximal ideal graphs. Comm. Algebra   42:6(2014)  2476-2483. DOI: 10.1080/00927872.2012.762924 (SCI)

 

54. Liu Q.，Wu Tongsuo and Ye M.  A construction of commutative nilpotent semigroups. Bull. Korean Math Soc. 50:3(2013) 801-809 DOI ：http://dx.doi.org/10.4134/BKMS.2013.50.3.801    (ISSN: 1015-8634)  (SCI)

                                                                                       

53. Wu Tongsuo,  Ye M.，Lu D.C. and Yu H.Y. On graphs related to co-maximal ideals of a           Commutative ring. ISRN Combinatorics    Vol. 2013, Article ID 354696, 7 pages

 

52. Lu D.C. and Wu Tongsuo. Endomorphism monoids of general split graphs. Ars Combinatoria Vol. CXI,  July (2013) 357-373. (ISSN: 0381-7032) (SCI)

 

51. Ye. M. and Wu  Tongsuo. Co-maximal ideal graphs of commutative rings.  J.  Algebra  Appl.  11:6(2012)   1250114 (14 pages)   DOI ：10.1142/S0219498812501149.    [Citations]  (SCI)

 

50. Wu Tongsuo,  Yu H. Y. and  Lu D.C.  The structure of finite local principal ideal rings.Comm. Algebra 40:12(2012) 4727-4738.  (A limited 50 copies of free e-prints at   https://www.tandfonline.com/eprint/SGrDvSnNJWDfvuRNgYcS/full  ) DOI: 10.1080/00927872.2011.618860.    [Citations] (SCI)

 

49. Lu D.C. and Wu Tongsuo. Regularity, \alpha*-invariants and the graded  module associated to a  filtration.  Comm. Algebra  40:10(2012) 3745–3752. [DOI: 10.1080/00927872.2011.594471] (SCI)

 

48. Yu H.Y., Wang Z.P.，Wu Tongsuo and Ye M.  Classification of some  \tau-congruence-free completely regular semigroups. Semigroup  Forum  84:2(2012) 308-322.   [DOI ：10.1007/s00233-011-9342-6]（published online 13 Sep. 2011）(SCI)

 

47. Chen L. and Wu Tongsuo.  On rings  R whose graphs   $\Gamma(R)$ satisfy a condition  $(K_ p)$. J.  Algebra  Appl. 10:4( 2011)  665-674. Doi: 10.1142/S0219498811004835    （Abstract）(ISSN: 0219-4988）(SCI)

 

46. Liu Q. and Wu Tongsuo. Zero-divisor graphs whose cores contain no rectangles.            Algebra Colloq. 18: 4(2011)  675---684  (SCI)

 

45. Liu Q. and Wu Tongsuo. Commutative rings whose zero-divisor graph is a proper refinement of a star graph. Acta Math.Sinica (ES）27:6(2011) 1221-1232 . (SCI)

 

44. D.C. Lu and T.S. Wu, The zero-divisor graphs of posets and an application to Semigroups, Graphs and Combinatorics  26(2010)  793–804. （ISSN: 0911-0119） Citations (SCI)

 

43. Lu D.C.  And Wu Tongsuo.  Topological characterizations of extending properties of rings.    Acta Math. Scientia 30B:4(2010) 1086---1092 .  (ISSN: 1003-3998) (SCI)

 

42. Chen L. and Wu Tongsuo.  Some refinements of star graphs whose semigroups S satisfy S3=0.  Comm. Algebra  38:7(2010), 2499-2512 .(A limited 50 copies of free e-prints at  https://www.tandfonline.com/eprint/S7iEA5t3nhqdav5U246G/full Doi: 10.1080/00927870903399885) (SCI)

 

41. Liu Q. and Wu Tongsuo. The structure of finite c-local rings.  Comm. Algebra Vol 37. No. 9  (2009)   3321-3336.(A limited 50 copies of free e-prints at  https://www.tandfonline.com/eprint/4aIH3IaiYx638U9suc4k/full )   [doi: 10.1080/00927870802502803]   (SCI)

 

40. Wu Tongsuo,  Liu Q. and Chen L.  Zero-divisor semigroups and refinements of a star graph.  Discrete Math. 309:8 (2009)  2510－2518.   [doi:10.1016/j.disc.2008.06.008]   Citations  (SCI)

 

39. Lu D.C.  And Wu Tongsuo. On bipartite zero-divisor graphs.  Discrete Math. 309:4(2009)  755－762.  [doi:10.1016/j.disc.2008.01.044] Citations (SCI)    

 

38. Wu Tongsuo and Chen L. Simple graphs and commutative zero-divisor semigroups. Algebra Colloq. 16:2(2009) 211-218  (ISSN :1005-3867) (SCI)

 

37. Liu Q., Ouyang B. and Wu Tongsuo. On principally quasi-Baer modules.  Journal Math. Research and Exposition 29:5(2009)  823-830

 

36. Lu D.C. and Wu Tongsuo. On normal ideals of exchange rings. Siberian Mathematical Journal. 49:4 (2008) 663－668 (ISSN: 0037-4466) [Click here for the Russian version，or see  Sibirskii Matematicheskii Zhurnal, Vol. 49, No. 4,  pp. 829—836, July—August, 2008.] (SCI)

 

35. Wu Tongsuo and Lu DC.  Sub-semigroups determined by the zero-divisor graph.             Discrete Math. 308:22 (2008)， 5122－5135. doi: 10.1016/j.disc.2007.09.032 .   Citations (SCI)

 

34. Lu D.C.  And  Wu Tongsuo. On endomorphism-regularity of zero-divisor graphs.            Discrete Math. 308:20 (2008)， 4811－4815. [doi:10.1016/j.disc.2007.08.057. ](ISSN: 0012-365X)     (SCI)

 

33. Wu Tongsuo and Cheng F.  The structure of zero-divisor semigroups with graph Kn 。K2 . Semigroup Forum 76:2(2008),  330-340. (SCI)

 

32. Lu D.C.  And  Wu Tongsuo. The zero-divisor graphs which are uniquely determined by neighborhoods.  Comm. Algebra 35:12(2007) ,  3855-3864 （ISSN: 0092-7872 Citations ）(SCI)

 

31. Wu Tongsuo and Lu D.C. The structure of a class of Z-local rings.  Sci. China, Series A.

          49:10(2006),  1297-1302.        {For a Chinese version please see   中国科学A辑，No. 8,

          2006,    865-869}  (SCI).

 

30. Wu Tongsuo and Lu D.C.   Zero-divisor semigroups and some simple graphs.  Comm. Algebra 34:8(2006), 3043-3052. [DOI: 10.1080/00927870600639948 .]    Citations (SCI)

 

29. Wu Tongsuo.  On directed zero-divisor graphs of finite rings.  Discrete Math. 296:1(2005), 73-86.   [DOI: 10.1016/j.disc.2005.03.006. ]  Citations (SCI)   

 

28. Zuo M. and Wu Tongsuo. A new graph structure of commutative semigroups. Semigroup Forum 70:1(2005), 71-80.  [ISSN: 0037-1912]Citations (SCI)

 

27. Wu Tongsuo and Chen P. On finitely generated projective modules and the exchange rings. Algebra Colloq.  9:4(2002), 433---444. (SCI)

 

26. Wu Tongsuo. Further results on finitely generated projective modules. Acta Math. Sinica (ES), 18:2(2002) 225---228.   { For a Chinese version please refer to   数学学报,  48:1(2005), 177}    (SCI)                                                           

 

25. Wu Tongsuo. Exchange rings with bounded index of nilpotence. Comm. Algebra 29:11(2001), 3089-3098.     [MR2002e: 16006.]     (SCI)

 

24. Wu Tongsuo. Exchange rings with general aleph-nought comparability.  Comm. Algebra 29:2(2001), 815-828.     [MR2002d: 16013]  Citations.    (SCI)

 

23. Wu Tongsuo. The power-substitution condition of endomorphism rings of quasi-projective modules. Comm. Algebra 28:1(2000), 407---418.  Citations (SCI)

 

22. Wu Tongsuo. Characterizing the weak stable range one condition by completions of diagrams. Journal Math. Research and Exposition 19:1(1999) 131-134. [zbMath 0938.16004]

 

21. Wu Tongsuo. On induced group homomorphisms.  J. Shanghai Jiaotong University   E4-1(1999)  65-67.

 

20. Wu Tongsuo. Endomorphisms of finitely generated modules. J. Nanjing University Math. Biq.  16:2(1999) 239—–242. [zbMath 0954.16025]   (in Chinese，with an  English summary)

 

19. Wu Tongsuo. On the stable range of endomorphism rings of quasi-projective modules. Comm. Algebra 6:1(1998)，139---146,    [zbMath 0902.16003.]      (SCI)

 

18. Wu Tongsuo. On endomorphism rings of regular modules. Acta Math. Sinica ( ES ) 14:3(1998),  115---120.  [MR99e: 16033 . zbMath 0908.16005.] For a Chinese Version please refer to  数学学报41:3(1998), 507.  (SCI)

 

17. Wu Tongsuo and Xu Y.H.  On the stable range condition of  exchange rings. Comm. Algebra 25:7（1997），2355—–2363.    MR98f: 16008. ZBL 0887.16006.   Citations (SCI)

 

16. Wu Tongsuo. K0-Groups of endomorphism rings of a class of artinian modules.  Journal of Mathematics (Wu Han) 17:1(1997) 127---130. [zbMath 0963.16502] [ in Chinese]

 

15. Wu Tongsuo. Global lifting of projective modules modulo Socles.   Chinese Science Bulletin 41:20(1996), 1673---1675   [MR98c: 16001.  zbMath 0863.16001. ]  For a Chinese version, please refer to  科学通报，41:19(1996), 1732 } (SCI)

 

14. Wu Tongsuo. Exchange rings whose primitive factor rings are artinian.   Algebra Colloq.   3:3(1996), 225—–230.  [MR97k:16009. zbMath 0857.16005] . [ISSN :1005-3867]  (SCI)

 

13. Wu Tongsuo and Tong W.T.  Stable range condition and cancellation of modules. Pitman Research Notes In Math. Series Vol. 346(1996), 98—–104 . [zbMath 859:16005 ]  Citations

 

12. Wu Tongsuo. Inner weak cancellation of modules.  J. Nanjing University Math.  Biq. 13:1(1996) 1—–4. [MR97f: 16011. ZbMath 0963.16502.]

 

11. Wu Tongsuo and Tong W. T.  Finitely generated projective modules over exchange rings. Manuscripta Math. 86:2(1995)， 149---157, MR96e:  16004. zbMath 824: 16002(1996) .Citations (SCI) [ISSN:  0025-2611]

 

10. Wu Tongsuo. On essentially supernilpotent rings and the dual. Comm.  Algebra 23:12(1995), 4473—4479   MR96i: 16034. ZBL.836(1996):16014. [ISSN: 0092-7872]   Citations (SCI)

 

9.  Wu Tongsuo. Weak cancellation of modules and qu-regular rings (in Chinese).  Acta Math. Sinica 38:6(1995)  746---751.   MR96k: 16011. ZBL844: 16006. Citations

 

8.  Wu Tongsuo. Endomorphism rings of artinian modules (in Chinese.) Chinese Ann. Math. 16A:2(1995)  217---222, MR96d:16034. ZBL833:16030

 

7.  Wu Tongsuo. Unit 1-stable range condition (in Chinese). Chinese Ann. Math. 16A:6   (1995) 760---768   MR96k: 16060. ZBL 0859.16006.  Citations

 

6.  Wu Tongsuo. Weak cancellation of modules and weak stable range one condition. J. Nanjing University  Math.  Biq. 11:2(1994) 109–116. [MR96g: 16005. ZbMath 0836.16004.]

 

5.  Chen H.X. and Wu Tongsuo. A Morita context related to Hopf module algebras.  J. Nanjing University  Math.  Biq. 11:1(1994) 39-43.   [ZbMath 821:16039 .]

 

4.  Wu Tongsuo. K0-Groups of weak regular rings and global dimension of weak noetherian rings. J. Nanjing University Math. Biq. 10:2(1993) 203-20. [Zbl 0829.16006. in Chinese.]

 

3.  Wu Tongsuo. On the radical equation R(An)=R(A)n. J. Yangzhou University 1(1991) 9-11. [ in Chinese].

 

2.  Wu Tongsuo. Some characterizations of simply-hereditary radical. J. Hebei Normal University 4(1990) 27-30.   [in Chinese]

 

1.  Wu Tongsuo. The Behrens radical of full matrix rings over associative rings. Chinese Science Bulletin. 1987(12) 959-960. [ in Chinese]

 

0.  Wu Tongsuo. The complemented radical of simply-hereditary weak super-nilpotent radical.   J. Yangzhou University 1-2(1987) 15-17. [ in Chinese]    (  Start from null; 加油！)