Nilpotent radical

The automorphism group of finite_dimensional solvable complete Lie algebra whose nilpotent radical is a Heisenberg algebra over the complex field C is given.

给出了复数域Ｃ上幂零根基为Ｈｅｉｓｅｎｂｅｒｇ代数的有限维可解完备李代数的自同构

In this paper, the derivation algebras of splittable Lie algebras with abelian nilpotent radicals are obtained.

确定了具有交换幂零根基的可裂Ｌｉｅ代数的导子代数，作为推论给出了具有交换幂零根基的完备Ｌｉｅ代数的结构。

In this paper,the authers prove that if H is a Heisenberg algebra,then there exists one and only one up to isomorphism solvable complete Lie algebra whose nilpotent radical is H,and give the realization of this kind of complete Lie algebras.

证明了给出一个Ｈｅｉｓｅｎｂｅｒｇ代数Ｈ，在同构的意义下存在且仅存在一个以Ｈ为幂零根基的可解完备Ｌｉｅ代数，我们给出了这类完备Ｌｉｅ代数的具体实现，并指出当ｄｉｍＨ＞３时，这类完备Ｌｉｅ代数是非极大秩可解完备Ｌｉｅ代数。

in this paper,the notions of nilpotent radical and quasi-nilpotent radical of Prings are introducted,some conditions of nilpotent radical exist are represented and quasinilpotent radical is Amitsur-Kurosh radical is proved.

定义了г－环的幂零根和拟幂零根，给出幂零根存在的若干条件，证明拟幂零根是Ａｍｉｔ－ｓｕｒ－Ｋｕｒｏｓｈ根，给出它的半单г－环的构造命题和г－模刻划。

The concept of nilpotent ideals of Malcev algebras,which is a generalization of the concept of nilpotent ideals of Lie algebras,is defined,the existence of a nil radical is proven,and the relationship between the nilpotent ideals of Malcev algebras and that of its standard construction is examined.

作为李代数的幂零理想的推广 ,定义了马尔策夫代数的理想 ,证明了对这样定义的幂零理想存在惟一的幂零根 ,并且研究了马尔策夫代数中的幂零理想与其标准构造 (李代数 )中的幂零理想之间的关系 。

The author has defined the nil radical of the symplectic termary algebra, investigated the relation of the nil radical and the solvable radical and discussed the relation of the two nil radicals of the symplectic ternary algebra and it s lie triple system.

给出了幂零的定义 ,得到了辛三代数的幂零根与可解根之间的关系和辛三代数与其生成的李三系的幂零根之间的关

In this paper, the Nil radicals and nilpotent radicals of split Lie algebras are sudyied.

对可裂李代数的Nil 根和幂零根进行研究 ,从结构和表示两方面给出了它们相等的两个条件 。

in this paper,the notions of nilpotent radical and quasi-nilpotent radical of Prings are introducted,some conditions of nilpotent radical exist are represented and quasinilpotent radical is Amitsur-Kurosh radical is proved.

定义了г－环的幂零根和拟幂零根，给出幂零根存在的若干条件，证明拟幂零根是Ａｍｉｔ－ｓｕｒ－Ｋｕｒｏｓｈ根，给出它的半单г－环的构造命题和г－模刻划。

Relationship of P-radical and Nil-radical of Finite-dimensional Restricted Lie Algebra

有限维限制李代数P-根基和幂零根基的关系

proper nilpotent element

真幂零元素，根元素

And element X=A is nilpotent.

元素X＝A是幂零的。

The base of primitive non-powerful symmetric sign pattern matrices with non-zero traces

迹非零的本原不可幂对称符号模式矩阵的基

An algebraic quantity that when raised to a certain power equals zero.

幂零一个代数值，其若干次幂等于零

The Finite Group that the Order of Maximal Nilpotence Subgroups are Prime Power

极大幂零子群的阶为素数幂的有限群

equal to zero when raised to a certain power.

其若干次幂等于零的。

We investigate some properties of theι- radical in lattice-ordered rings(ι- rings). Specially we identify several classes ofι- rings in which the set of all nilpotent elements iS anι- ideal.

研究了格序环的ι根的一些性质,特别给出了所有幂零元的集合是ι理想的几类格序环.

Cohomology and Nullcones of Jacobson-Witt Algebras;

Jacobson-Witt代数的上同调与幂零锥

Primitiveness of Character Triples and X-Nilpotent Group;

特征标三元组的本原性和X-幂零群

Using Ⅱ-Jordan Nilpotent Matrices over Finite Fields to Construct Cartesian Authentication Codes;

利用Ⅱ-Jordan型幂零矩阵构造Cartesian认证码

The p～＊-Nilpotency and θ-Pairs for Subgroups on Finite Groups;

有限群的p～＊-幂零性和子群的θ-子群偶

Some Results on the Weak Nilpotent Element of N（2，2，0）Algebra;

关于N(2,2,0)代数的弱幂零元的若干结果

Polynomial Maps with Additive-nilpotent Jacobian Matrix

带有可加幂零Jacobi矩阵的多项式映射

Finite Nilpotent Groups with Automorphism Group of Order 4p~3

具有4p~3阶自同构群的有限幂零群

Finite nilpotent groups with automorphism group of order 4p~2q

具有4p~2q阶自同构群的有限幂零群

Maximal n-Nilpotent Lie Ideals of Nest Algebras

套代数中的极大的n-幂零Lie理想

F-S-Supplement of the Mininal Subgroups and p-nilpotentcy of Finite Groups

极小子群的F-S-补与有限群p-幂零性