One is that let φ be a representation on a finite dimensional associative algebra A , its representative matrix be T(a),and there exist an element a∈Z(A), a≠0,where Z(A) is the centralizer of A, such that T(a)≠0 and det T(a)=0,then φ is reducible.
给出有限维结合代数上表示可约性的两个判别法。
By using the fundamental theorem of algebra,it is proved that there exists at least one root for a special class of polynomial equation with coefficients in a subspace of the associative algebra which is the base associative algebra of Clifford algebra.
利用代数基本定理,证明以Clifford代数所基于的结合代数的一子空间作系数空间,一类特殊的多项式方程在该子空间中至少存在一个根。
Let L_C=νi=1Zc_i,L_D=νi=1Zd_i be lattices,L=L_C+L_D be a lattice with symmetric bilinear form,A be an associative algebra generated by e_α,d_i with relations e_0=1,e_(α+β)=e_αe_β,d_ie_α-e_αd_i=(d_i,α)e_α,d_id_j=d_jd_i(α,β∈ L_C,1≤i,j≤ν).
设LC= νi=1Zci,LD= νi=1Zdi 为格,L=LC+LD 为具有对称双线性形式(·,·)的双曲格,A为由eα,di 及关系e0=1,eα+β=eαeβ,dieα-eαdi=(di,α)eα,didj=djdi 生成的结合代数(α,β∈LC,1≤i,j≤ν)。
As a consequence of the above result,we have that implicative semilattices form an algebraic variety.
作为一个推论给出:蕴涵半格构成一个代数簇。
,x n], P=Q the root ideal of Q and J the subset of ring assume Q∩J≠ , then the algebraic varieties of idea quotient V(Q∶J)= .
设Q是多项式环k[x1 ,x2 ,… ,xn]中的P 准素理想 ,P =Q是理想Q的根理想 ,J是k[x1 ,x2 ,… ,xn]的子集 ,若Q∩J≠ ,则Q对J的商理想Q∶J的代数簇V(Q∶J) = ;若Q∩J = ,则Q∶J的代数簇V(Q∶J) =V(Q∶J) ;若P∩J= ,则V(Q∶J) =V(Q) 。
In this paper by applying some equivalent formulas in first-order logic,this problem is transformed into one which checks whether another quasi-algebraic variety is empty.
判定拟代数簇的包含关系问题不能由计算其相应的饱和理想来确定 。
Representations of Vertex Operator Superalgebras and Associative Algebras
顶点算子超代数及相关的结合代数的表示
Construction of q-Lie Algebra by association Algebra and the Classification of Low Dimension q-Lie Algebra
由结合代数构造q-李代数及低维q-李代数的分类
This paper introduces theσ_ automorphism for finite dimensional commutative associative algebras and studies the structure ofσ_ semisimple algebras andσ_ nilpotent algebras.
通过引入有限维交换结合代数的σ自同态映射，研究了σ半单代数和σ幂零代数的结构。
The Relation between BCH_algebra and Generalized Associative BCI-algebra;
BCH-代数与广义结合BCI-代数的关系
Multiplication in ordinary arithmetic or algebra is associative.
普通算数或代数学中的乘法是结合的。
Solving Several Kinds of Algebra Problems by Using the Number Shape Union Method;
利用数形结合方法求解几类代数问题
P-solvable Restricted Lie Colour Algebras and the Basic Theory of Associative Lie Colour Algebras;
P-可解限制李colour代数与结合李colour代数基本理论
Quasi-associativeΩ-fuzzy ideals of BCH-algebras;
BCH-代数的拟结合Ω-模糊理想(英文)
How to Enbody the Combination of Higher and Elementary Mathematics in Higher Algebra;
在高等代数教学中如何体现“高初结合”
The Argument Distribution of The Multiple Value and the Derived Functions of Integral Functions with Iterated Order;
迭代级整函数的结合于导数与重值的辐角分布
Lie algebra structure on Virasoro algebra
Virasoro代数的Hom-李代数结构
Blending Algebraic Surfaces by the Method of Dividing Boundaries and Filling Holes with S-patches;
代数曲面混合—切分结合S曲面片补洞方法
An Organic Union between Algebra and Geometry in Geometric Teaching;
代数与几何的有机结合是解析几何教学的关键
On the cohomology theory for associative superalgebra adjoining an identity element;
具有相伴单位元的结合超代数的上同调
The Representation With Function of Conditional Fuzzy Events and the Structure of the Set of Conditional Fuzzy Events;
条件模糊事件的函数表示及条件模糊事件集合的代数结构
By using the concept of iterated order, we investigate the argument distribution of the multiple value and the derived functions of integral functions with irerated order.
利用整函数的迭代级的概念,研究了迭代级整函数的结合于导数与重值的辐角分布。
Effects of Ratio of Structural and Nonstructural Carbohydrates in Diets on Digestion and Metobolism as Well as Rumen Metabolic Parameters for Sheep;
饲粮结构与非结构碳水化合物比例与绵羊消化代谢及瘤胃代谢参数
Hopf*-algebra Structures on Some Hopf Algebras;
某些Hopf代数的Hopf*-代数结构