极大理想

Theorem 2.2.44 Let R be a reduced left morphic ring, if R satisfies ascending chain condition on right annihilators, then every maxmal left ideal of R is a direct summmand of R.

定理2.2.44设R是约化的左morphic环，若R对右零化子满足升链条件，则R的每一个极大左理想L都是R的一个直和项。

As an ideal material for banding, nylon bar to our daily lives has brought great convenience.

作为一种理想的捆扎材料，尼龙扎带给我们的日常生活带来了极大的方便。

Any castle with a Caravansary is a preferred destination for desert trade, greatly increasing the taxable income in the region.

建有客栈之城堡将是任何沙漠商队的理想宿营地，从而极大提高了城堡贸易。

Every maximal ideal of every commutative ring with identity is a prime ideal.

带有单位元的交换环的任何极大理想是素理想。

The homogeneous calibrator and ideal material calibrator are considered respectively. From the optimal results" analysis and comparison, we can see that the ideal material calibrator improves greatly the cooling uniformity of plastic profile by changing the cooling channel"s location, size, number and adjusting calibrators material distribution.

分别考虑均质定型模和理想材料定型模，从优化结果分析、比较可以看出，理想材料定型模通过改变冷却水道的位置、尺寸和数量以及调整其材料分布规律，极大地改善了塑料型材的冷却均匀性和冷却效率。

In this paper, we first give the structure of R, including its maximal, minimal right ideals and the structure of its Jacobson radical, socle and singular right ideal as well.

在本文中，我们首先给出了R的一些结构，包括它的极大、极小右理想和它的Jacobson根、基座以及奇异右理想，顺便列举了它们的相关结果。

The first chapter, main instead " duo-ring " condition of " every maximal left ideal is GW-ideal " condition,study strongly regularities of GP-V-ring on this condition.lt is shown that (1) R is strongly regular iff R is left GP-V-ring whose maximal left ideals are GW-ideal.(2)R is strongly regular iff R is left GP-V-ring whose maximal right ideals are GW-ideal. The second chapter, generalize some results of GP-V-ring to GP-V-ring, discuss regularity of GP-V-ring.It is shown that (1) R is left self-injective regular with non-zero socle iff R is left GP-V -ring with Soc = Soc and R contains an injective maximal left ideal.(2)R is regular ring and every maximal essential left ideal is ideal iff R is left GP-injective left GP-V -ring and every maximal essential left ideal is ideal.

第一章主要将"duo-环"条件替换成"每一极大左理想是GW-理想"条件，研究在此条件下，GP-V-环的强正则性，证明了：(1)R是强正则环当且仅当R是左GP-V-环且R的每一极大左理想是广义弱理想；(2)R是强正则环当且仅当R是左GP-V-环且R的每一极大右理想是广义弱理想，第二章，主要将GP-V-环上一些结果推广到GP-V′-环上，讨论GP-V′-环的正则性，证明了：(1)R是左自内射正则环且Soc≠0当且仅当R是包含内射极大左理想的GP-V′-环，且Soc=Soc；(2)R是正则环且每一极大本质左理想是理想当且仅当R是左GP-内射的左GP-V′-环且每一极大本质左理想是理想。

Every prime ideal of R is maximal ideal.

2R的每个素理想均为极大理想。

Using the presentation, suppose that M is the maximal ideal of a commutative local domain R and R/M=F〓 is a finite field with q elements, a generating set of elements at most is obtained for K=Coker K〓

设M为交换局部整环R中极大理想，R/M〓F〓为q元有限域，由这个表现得到了K=Coker的一个至多含有个元素的生成元集。

Conversely, in terms of the correspondence between the pure state and the maximal left idea, we get that if each hereditary C(superscript *)-subalgebra (or one-sided closed ideal) of A is a closed ideal in A, then A must be Abelian.

反之，利用C-代数A上的纯态与A中极大左理想的对应关系，得到了：若A中的每一个遗传子代数都是它的双侧闭理想，则A一定是交换的。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。