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Faith猜测与余环的同调理论
  • 项目名称：Faith猜测与余环的同调理论
  • 项目类别：面上项目
  • 批准号：10571026
  • 申请代码：A010205
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2008-12-31
  • 项目负责人：陈建龙
  • 负责人职称：教授
  • 依托单位：东南大学
  • 批准年度：2005
中文摘要：

1939年Nakayama在研究Frobenius代数时引入了QF环的概念。此后，QF环吸引了众多代数学家的兴趣，尤其是环论和Hopf代数专家的兴趣，他们从不同角度给出了QF环的刻画，并围绕QF环提出了众多问题，其中最为著名的是Faith提出的三大猜测(FGF猜测，Faith-Menal猜测，Faith猜测)以及Nicholson和Yousif提出的21个具有挑战性的问题（至今仍未解决）。QF环是域上有限群的群代数的推广，而群代数是一种典型的Hopf代数。因此自然而然地提出了QCF余代数的概念。本项目拟围绕Faith三大猜测给出QF环新的性质刻画，推进猜测研究进程，回答Nicholson与Yousif的部分问题。同时刻划QCF余环，并用挠理论与余挠理论研究余环的同调性质，作为应用，将给出著名的Drinfel'd量子偶新的结构性质，进一步讨论物理场上量子杨-Baxter方程解的代数特性。

中文主题词： QF环;FGF环;Johns环;QCF余环;Drinfel'd量子偶
成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
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期刊论文
Quasi-Armendariz modules
On strongly clean matrix and triangular matrix rings
$I$-semi-$\pi$-regular rings
Exchange general rings
Modules which are subisomorphic to their envelopes
Larson-Sweedler theorem and some properties of discrete type in ($G$-cograded) multiplier Hopf algeb
A note on relative flatness and coherence
$\pi$-morphic rings
p.p. properties of group rings.
On $(m,n)$-coherent modules and preenvelopes
Generalizations of morphic group rings
When is the 2X2 matrix ring over a commutative local ring strongly clean
Strongly clean power series rings
Extensions of injectivity and coherent rings.
On characterizations of Drazin inverse
Morphic Property of Extension Rings
Asympotic Bound on Binary Self-Orthogonal Codes
Extensions of McCoy rings
On $\bigoplus$-supplemented Modules and H-supplemented
Characterizations of QF rings
On the twisting and Drinfeld double for multiplier Hopf algebras.
On n-semihereditary and $n$-coherent rings
On strong Goldie dimension
On Relatively Semi-projective and Direct-projective
Group rings in which every element is uniquely the sum of a unit and an idempotent
New characterizations of quasi-Frobenius rings
An approach to the Faith-Menal conjecture
2-clean rings
On UR-rings
Rings satisfying UR-stable range
On Relatively Direct-injective and Continuous
Moritacontexts,pi-Galois extensions or Hopf pi-coalgebras.
Coquasitriangular Hopf group algebras and Drinfeld co-doubles.
Twisting theory for weak Hopf algebras.
Blattner-Cohen-Montgomery's duality theorem for (weak) group smash products
New braided?crossed categories and rinfel'd quantum double for weak Hopf group coalgebras,
The genelarized C.M.Z.-Theorem and a Drinfeld double construction forWT-coalgebras and graded quantu
Differenttial Calculi on Quantum Groupoids,
Morphic group rings
Rings in which elements are uniquely the sum of an idempotent and a unit that commute
Group corings.
$\alpha$-skew Armendariz modules and$\alpha$-semicommutative modules
Zip modules
Properties of Modules and Rings Relative to Some Matrices
On $FI$-extending Rings and Modules
Making the category of entwined modules into a braided monoidal category
Lax group corings
On group crossed products
On Braided Lie Structures of Algeras in the Categories of weak Hopf bimodules
Singular solutions to the quantum Yang-Baxter equations
On semilocal group rings.
A note on clean rings
The structure of ring $R[D,C]$ and its characterizations
Extensions of strongly $\pi$-regular general rings
A question on McCoy rings
Extensions of morphic rings
On strongly clean general rings
Relatively injective modules with respect to torsion theory
On VNL-rings and n-VNL-rings
态射和的Drazin逆
I-semi-π-regular Rings
构造群缠绕模范畴成为辫子张量范畴
关于r-semiclean环
F-本质子模与F-多余子模
相对于余挠对的维数
弱Hopf代数的扭曲理论
On minimal quasi-injective modules and strong Kasch modules
弱M—Armendariz环
Twisting theory for weak Hopf algebras
关于特殊的F-预复盖与F-预包络
强π-正则一般环的扩张
构造entwined模范畴成为辫子张量范畴
On FI-extending Rings and Modules
Hopf π-余代数上Doi-Hopf模的Maschke型定理（英文）
定数截尾下 Burr Type XII 分布的统计推断
关于强Clean一般环
On Semilocal Group Rings
关于均值单边检验的局限性
On Relatively Semi-projective and Direct-projective Modules
齐次半局部群环
Hopf Algebras in Group Yetter-Drinfel＇d Categories
具有UR-稳定度的环
拟半-clean环的若干研究
Exchange一般环
On （m, n）-Coherent Modules and Preenvelopes
Monoidal Entwined模范畴上的张量积恒等式
关于F-覆盖的存在性
著作
线性代数
线性代数习题解答
陈建龙的项目
环的相关正则性及其应用
期刊论文 54 会议论文 1
凝聚环的同调理论及其应用
广义逆理论与偏序结构
表示论中的逼近理论与Grothendieck群
期刊论文 2
第四届中日韩国际环认论会议
正则性及广义逆理论
期刊论文 11