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- Let D_(l+1)(R) be the orthogonal Lie algebra over a commutative ring R with 2 invertible and m_1 an l+ 1 upper triangular matrix. 设D_(l+1)(R)表示2为单位交换环R上的2(l+1)阶正交李代数。 若记m_1是R上的l+1阶三角矩阵，而是D_(l+1)(R)可解子代数。
- A commutative ring with unity having no proper divisors of zero, that is, where the product of nonzero elements cannot be zero. 整环，整域：一个单位元素都不是零的真约数，即，非零元素的乘积不为零的交换环
- Let R be a commutative ring without zero-divisor,R is called a quasi-valuation ring,if it contains a non-zero element a such that any non-zero element of R divides a power of a. 一个无零因子的交换环R称为拟赋值环,如果R中有一个非零元素a,使得R的任意非零元都整除a的某个方幂。
- The fundamental theorem of arithmetic is an important and basic theorem of theory of number and plays an important role in modern commutative ring theory. 算术基本定理是初等数论中一条非常基本和重要的定理,它所体现的唯一因子分解的思想,在现代交换环理论中起着非常重要的作用。
- See invertible matrix for more.More generally, a square matrix over a commutative ring R is invertible if and only if its determinant is invertible in R. 更一般地，一元素在一可交换环R内的方阵是可逆的若且唯若其行列式在R是可逆的。
- L_Z associated with finite-dimensional simpleLie algebras and affine Lie algebras of type k =1 over a commutative ring withidentity were defined by J. Hurley in 1969 and 1981 respectively, and theirideal structures were worked out there. Hurley在1969年与1981年分别对有限维复单李代数及k=1的仿射李代数L研究了相应的Chevalley代数L_R=RL_z的理想结构。
- Many people know mathematics, at least they know commutative rings when they are married. 其实很多人都会数学，最少在他们结婚的时候会交换戒指。
- In this paper, we study the subalgebra structure of the general linear Lie algebras over commutative rings. 摘要本文研究了含幺可换环上一般线性李代数的子代数结构。
- This result will be helpful for us to know the subgroup structure of corresponding classical groups over commutative rings. 并且有利子研究可换环上相应的典型群的子群结构。
- Problems of "pushdown" and "pullback" on a commutative ring 交换环上的“下降”问题和“上升”问题
- Endomorphisms of a Finite Commutative Ring with Identity 有限交换幺环的自同态
- She had the sapphire set in a gold ring. 她把那枚蓝宝石镶在金戒指上了。
- The diamond ring dazzled with brilliancy. 这只钻石戒指闪耀夺目。
- She wears a diamond ring on her left hand. 她左手上戴着一枚钻石戒指。
- Our family reunions are always three ring circus. 我家合家团聚的场面总是热闹非凡。
- theory of general commutative rings 一般交换环论
- SVERAL RESULTS ON V-VALUATIONS OF COMMUTATIVE RINGS 关于交换环的V-赋值的几个结果
- I am sorry-she's out. Can you ring again later? 对不起－她出去了。你过些时候再打电话来好吗？
- The boys and girls made a ring round us. 男孩和女孩围着我们站了一圈。
- Compound adjoint matrices over commutative rings 交换环上的复合伴随矩阵
