查询词典 finitely generated ideal

In chapter 1, one type of maximal subgroups in symplectic groups overpolynomial rings are obtained. Let F be a field, R = F be a ring of polynomial in one variable over F, m be a positive integer, f eF and S be the ideal of R generated by -f, We define:, then G is a maximalsubgroups of Sp(2m,R).

在第一章中，得到了多项式环上辛群的一类极大子群：设F是一个域，R=F是域F上关于λ的一元多项式环，m是一个正整数，f∈F，S是R的由λ-f生成的理想，则是Sp(2m，R)的一个极大子群。

If R andits ideal I satisfied the condition 〓 satisfied〓,there exists 〓 such that 〓.then K〓is generated by elements of type Dand C.

证明了当环R及其理想I满足条件〓（即对a，b∈I，且aR+(1+b)R=R，一定存在t∈U使得a+(1+b)t∈U时的情况，〓可由D和C生成。

As one of common pioneer plants growing on mine tailings in Yunnan Province, Rumex dentatus has generated metal tolerant ecotype and could therefore be treated as an ideal experimental material for stress ecology study.

作为云南矿区废弃地常见的先锋植物，齿果酸模已形成对重金属污染的耐性生态型，是理想的逆境生态学研究实验材料。

The results indicate that, using the PCMTS cores as the actuators, an ideal deflection of the sandwich beam is generated and the vibration of the sandwich beam is suppressed effectively.

结果表明，利用PCMTS作为驱动元件，夹芯梁获得了比较理想的变形量，其振动也能得到较为有效的控制，因此是一种很有应用前途的驱动方式。

Second, we think about the Conjecture(Conjecture8.7,Conjecture8.23;[2]Conjec-ture2.3) and prove that some particular ideals have the same graded Betti numbers via shifting operations,that s,.if is a simpcial complex and I is a monomial ideal generated in one degree,we have that...

后一部分的主要结论是：针对J.Herzog提出的猜想([1]猜想8.7，猜想8.23；[2]猜想2.3)，证明了当I_Δ为同一次数生成元生成的稳定理想时，对i，j，有β_=β_。当I_Δ为无平方分量线性理想，特别地当I_Δ是弱稳定理想时，对i，j，有β_=β_=β_。

Second, we think about the Conjecture(Conjecture8.7,Conjecture8.23;[2]Conjec-ture2.3) and prove that some particular ideals have the same graded Betti numbers via shifting operations,thats,.if is a simpcial complex and I is a monomial ideal generated in one degree,we have that ij = ij, for i.j.

后一部分的主要结论是：针对J.Herzog提出的猜想([1]猜想8.7，猜想8.23；[2]猜想2.3)，证明了当I_Δ为同一次数生成元生成的稳定理想时，对i，j，有β_=β_。

There is no limit to what this law can do for you; dare to believe in your own idea; remember that Nature is plastic to the ideal; think of the ideal as an already accomplished fact.

这条法则可以为你做任何的事情。大胆地相信你自己的理想吧！要记住，人的天性是能够被理想塑造的，你只要把理想当作既成事实去想它。

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

The experimental results show that:(1) for ideal spheres, the attenuation coefficient of velocity is constant, the air drag coefficient is slightly affected by the initial velocity and is a linear function of initial velocity, and (2) for real fragments formed by a warhead, the flight performances are different from ideal spheres, the air drag coefficient is affected by the flight velocity and is a linear function of flight velocity.

实验结果表明：(1)对于理想球形钨合金破片，在同一初始速度条件下，衰减系数为常数，空气阻力系数与初始速度有关，两者成线性关系；(2)对于经历爆轰驱动的球形钨合金破片，由于有轻微的质量损失和变形，速度衰减规律与理想球形钨合金破片有明显的区别，空气阻力系数与飞行速度有关，两者成线性关系。

Residents may choose their ideal beachfront property, and select between the two designs for their ideal custom residence.

居民可以选择自己的理想的海滨财产，并选择两者之间的设计定制的理想居所。

The receding calculations and experiment analyses in this subject are built on the blood cast of pig tongue.

本研究课题的前期工作是采用猪舌血管铸型模拟人舌而进行的数值计算与实验分析。

"Each human infection constitutes an opportunity for genetic modification of the virus through reassortment, mutation, or both...."

&每一次人类的感染都暗藏着一次基因修改的机会，无论是通过病毒的整合、突变或者兼而有之。。。。&