n+1维n-Lei代数的导子代数

本文给出了n 1维n-Lie代数的导子代数的结构，以及导子的具体表示形式．     

BCK—代数的模糊理想的若干性质

运用模糊点的概念研究BCK代数的模糊理想等一些基本概念和性质,建立它与利用隶属函数和水平截集等常见刻画方式之间的关系。     

π-模余代数与π-模余理想

主要讨论局部有限维的Hopfπ-代数H上π-模余代数与π-模余理想.给出了π-H-模余代数与π-H~*-余模代数之间的对偶关系,得到了π-H-模余理想的一个充分必要条件.     

环中关于理想同余的粗糙集的性质

讨论了环中由理想同余关系所决定的下、上近似的一些特殊性质．     

N(2,2,0)代数的T-模糊子代数和T-模糊理想

为了深入研究N(2,2,0)代数的代数结构,在N(2,2,0)代数中引入了T模糊子代数和T模糊理想的概念,进一步讨论了它们的性质.分别给出了N(2,2,0)代数的模糊子代数和模糊理想与子代数和理想的关系.证明了N(2,2,0)代数的两个T模糊子代数的模交也是T模糊子代数,而N(2,2,0)代数的两个T模糊理想的模交也是T模糊理想.     

李Rinehart代数的子代数若干性质

本文主要把李代数的c-可补、E-代数的性质以及Frattini理论推广到更为广泛的李Rinehart代数,得到它们的若干性质,给出了可解李Rinehart代数的一个必要条件.同时,分别获得判断c-可补李Rinehart代数和E-李Rinehart代数的一个充分必要条件.     

5维幂零李代数的导子代数的结构

对维数为5的所有幂零李代数的导子代数进行了研究,按照其分类分别给出了9种互不同构的导子代数的结构。     

软代数的理想和同余关系

本文刻划了使软代数Ｆ的任意二元ａ，ｂ在一个同余类的最小同余关系（定理１），Ｆ的理想可以成为某个同余关系的核的充分必要条件（定理２），以Ｆ的同余理想Ｉ为核的最小和最大的同余关系（定理３）．     

软代数的同余理想

本文以软代数Ｆ的真积分解为工具，得到的主要结果是，如果软代数Ｆ的每信满足条件Ｉ∩Ｉ’＝Φ的理想Ｉ都是同余理想。则Ｆ是既约软代数，在既约的情况下，给出了软代数Ｆ的每个满足条件Ｉ∩Ｉ‘＝Φ的理想Ｉ都是同余理想的一个充分条件。从而初步解决了文「１」的结尾提出的一个问题。     

Kleene代数的诱导子代数及理想

由于逻辑学研究的需要 ,Kleene代数理论的重要性已越来越明显 .本文主要研究了Kleene代数的子代数及理想的一些性质 ,得到了一些比较好的结果 .     

Borel Subalgebras of Schur Superalgebras

It is proved that any Schur superalgebra is representable as a product of two Borel subalgebras of that superalgebra, which are symmetric w.r.t. its natural anti-isomorphism (Bruhat-Tits decomposition). This readily implies that any simple module is uniquely defined by its highest weight, and all other weights are strictly less than is the highest under the dominant ordering. It is stated that the fundamental theorem of Kempf, which is valid for all classical Schur algebras, might be true for superalgebras only if they are semisimple. Nevertheless, a weaker theorem of Grothendieck holds true for superalgebras since Borel subalgebras are quasihereditary. Also we formulate an analog of the Donkin-Mathieu theorem for Schur superalgebras, and show that it is valid in the elementary non-classical case, that is, for the algebras S(1|1, r).__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 305–334, May–June, 2005.     

拟遗传代数的Exact Borel子代数与主子代数

本文利用exactBorel子代数刻划了遗传代数,给出了basic拟遗传代数的主子代数是exactBorel子代数的充分必要条件．     

AF代数中子代数间等距代数同构的扩张

本文证明了具有二次交换子性质的ＡＦ代数中的子代数间的等距代数同构可以扩张成其包络Ｃ＊代数的＊同构．由此肯定地回答了［４］中２．１２提出的问题．     

Freeness of Quasi-Hopf Algebras Over Right Coideal Subalgebras

We will generalize Skryabin's Freeness Theorem [11 Skryabin , S. ( 2007 ). Projectivity and freeness over comodule algebras . Trans. Amer. Math. Soc. 359 : 2597 – 2623 .[Crossref], [Web of Science ®] , [Google Scholar]]to quasi-Hopf algebras. We will show that for a finite dimensional quasi-Hopf algebra H and a right coideal subalgebra K ? H all (H, K)-quasi Hopf bimodules are free K-modules, in particular, H is a free right and left K-module.     

PBW-bases of coideal subalgebras and a freeness theorem

Let be a character Hopf algebra. Every right coideal subalgebra U that contains the coradical has a PBW-basis which can be extended up to a PBW-basis of If additionally U is a bosonization of an invariant with respect to the left adjoint action subalgebra, then is a free left (and right) U-module with a free PBW-basis over U. These results remain valid if is a braided Hopf algebra generated by a categorically ordered subset of primitive elements. If the ground field is algebraically closed, the results are still true provided that is a pointed Hopf algebra with commutative coradical and is generated over the coradical by a direct sum of finite-dimensional Yetter-Drinfeld submodules of skew primitive elements.

     

偏倾斜模和倾斜模的分次与非分次性质

This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.     

关于模的最大有理扩张

ｉ）设Ｍ_ｉ为一族左Ｒ－模,记Ｍ_ｉ为Ｍ_ｉ的最大有理扩张,本文首先考察了∑⊕Ｍ_ｉ和∑⊕Ｍ_ｉ之间的关系,并证明了如对环Ｒ上任何一族模上述两者相等的充要条件是环Ｒ上每一个模都有理完全．ｉ）利用ｉ）研究了无零因子环上模的最大有理扩张,得到了一些结果．     

幂零矩阵子代数

本文较详细地描述了幂零矩阵子代数,并且获得了一些有趣的结果.     

Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.