1) multiplicative group
乘群
1.
In the multiplicative group,Hilbert definites an operation between a and b,and it denotes by the so-called Hilbert symbol(a,b).
在乘群k*中,希尔伯特定义了一种两个元素a,b之间的运算(a,b),称为希尔伯特符号,在此我们利用已经推得的(a,b)简单运算公式及性质,采用指数α,β,仅由它们的模2的剩余类决定这一特性,将α,β分成3种情形,根据乘群k*的性质、Legendre符号性质及p进方程的理论,对它的计算进行讨论。
2.
Because all elements of the multiplicative group F~*_p are square ,Gauss by that has proved the quadratic reciprocity law(l/p)=(p/l)(-1)~ε(l)ε(p) of Legendre s symbol in the finite field.
如果乘群Fp*的子集S满足Fp*是S和-S的和,那么S可取为S=1,2,…,p-12的特殊形式。
2) multiplier
[英]['mʌltɪplaɪə(r)] [美]['mʌltə'plaɪɚ]
乘数;乘群
3) group multiplication
群乘表
1.
By using stereographic projection of each point group,all symmetry operation and generating operation of the point groups are listed,and group multiplication table of maximal proper point group 822 is filled in.
运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表。
2.
All symmetry operation and generating operation of the point groups were listed,and their group multiplication table of maximal proper point group 10 22 was filled in.
绘出了各点群的极赤投影图;列出了各点群的所有群元和生成元;填写出了最大的固有点群10 22的群乘表。
3.
By using stereographic projection of each point group,all symmetry operation and generating operation of the point groups were listed,and group multiplication table of maximal proper point group 822 was filled in.
从理论上对准晶体中十二方晶系各点群进行了研究,绘出了十二方晶系7个点群的极赤投影图;列出了各点群的所有对称操作及生成操作;填写出了其中最大固有点群12 22的群乘表;在自定义的十二方坐标系中,导出了十二方晶系各点群所有对称操作的矩阵,这48个3×3矩阵的矩阵元有7种可能取值:0,±1,±2,±3,而3恰恰是反映十二方晶系准晶体所具有的准周期平移序的无理数。
4) multiplier groups
乘子群
5) multiplicative semigroup
乘法半群
1.
By a system of linear equations on multiplicative semigroup,we present a general mathematical method to solve the inverse lattice problems in physics.
用乘法半群上的线性方程组来求解晶体原子间对势反演的逆问题。
2.
In this paper, it is proved that if n≥2 and R is an effective semiring or a semiring in which all idempotents are central elements, then Φ:Tn(R)→Tn(R) is a multiplicative semigroup automorphism if and only if there exist a invertible G∈Tn(R) and a semiring automorphism τ of R such that Φ(A)=G-1τ(A)G for all A=(aij)n×n inTn(R).
证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G。
6) adjoint semigroup
圈乘半群
1.
It is proved that the adjoint semigroup of a π regular ring is a π regular semigroup.
证明 π正则环的圈乘半群是 π正则半群 。
2.
Rings with a completely regular generalized adjoint semigroup are characterized.
刻画具有完全正则的广义圈乘半群的环。
3.
This note deals with the regularity of the adjoint semigroup of a ring.
研究环圈乘半群的正则性。
补充资料：乘法群
乘法群
multiplicative group
乘法群[md石函口触，，，;M拯mn~皿明印y-皿a]，除环上的 给定除环(skew一倪记)中除零元外的所有元素在该除环的乘法运算下形成的群.域的乘法群是Abel群. 0 .A.玩a肋a撰【补注】带有限非零特征的除环的有限乘法子群是循环群，特征零的情况则不然.只有有限多偶数阶群，却有无限多奇数阶群，后者的极小阶是63.分类已在【AI]中给出.在证明一类Tits二择一性(Ti招司t肛na-tive)时，有类似的问题:除环的乘法群的任一有限正规子群含一自由非循环群或为一有限可解群且有一到除环上的线性群的扩张.某些情况是已知的，例如【A2].
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条