自同态环

Prove that the endomorphic ring of any simple module is a division ring.

假如非零模 M的子模仅有零子模和自身，那么称M为单模，证明单模的自同态环为除环。

In section one, we study regular cu-rings by use of full elements in rings, and give some equivalent conditions for the endomorphism ring of quasi-projective modules and quasi-injective modules to be a cu-ring.

在第一部分，我们利用环中的完全元对正则cu-环进行刻画，并给出了拟投射模和拟内射模的自同态环是cu-环的一系列等价条件。

Moreover, we define weak principally quasi-injective modules and study Jacobson radical of endomorphism ring of weak principally quasi-injective modules.

另外我们还在主拟内射R-模的基础上定义了弱主拟内射R-模，利用零化子对弱主拟内射模上自同态环的Jacobson根的性质进行了讨论。

Finally, sufficient and necessary conditions for endomorphism rings of some special modules to be semi-π-regular are given.

最后，我们对半π正则环作了一定的研究，给出了一个直投射模的自同态环是半π正则环的充要条件。

Firstly, an equivalence proposition of right qpm-injective module is discussed, and when the endomorphism of right qpm-injective module is right pm-injective ring is observed.

首先，讨论右qpm-内射模的一个等价命题，以及在什么情况下，右qpm-内射模的自同态环是右pm-内射环。

We give a theorem for the stable range of endomorphism rings of finitely generated projective modules over a formal triangular matrix ring T when T is an exchange ring.

2.6节对有有限exchange性质的形式三角矩阵环T给出了有限生成投射T-模的自同态环有稳定度n的一个具体关系。

Finally, it is proved that any semimodule over complemented semirings must have a ζ_s-injective hull and the complemented semiring must be the rPP semiring and the endomorphism semiring of every principal right ideal is still complemented semiring.

最后指出任一可补半环上的半模必存在内射包络、可补半环必是rPP半环且对于可补半环的任一主右理想的自同态集仍是可补半环。

Due to the inspiration of maximal injective module by professor Wang Ming-yi, in chapter two, we introduce the conception of max-projective modules, discuss its properties, applications: the primitive relations between rings and endomorphism rings, an equivalence that is surrounding strongly V.N. rings.

受汪明义教授引进极大内射模概念的启发，在第二章中我们引进了极大投射模的概念，由此讨论了它的一些性质及其应用：环与自同态环之间的本原性关系；强正则环的一个等价刻划；并在环为交换和非交换的情形下分别应用有限表现模的极大投射性得出了SF环和Von Neumann正则环的关系。

If M is self-generator, then the endomorphism of right qpm-injective module M is right pm-injective ring. Finally, the properties of the endomorphism of right qpm-injective module are discussed and obtain some applications.

且仅当如果ker=ker，其中s，t∈S=End，那么Ss=S_t；(2)如果右R-模M是自生成子，那么右qpm-内射模M的自同态环是右pm-内射环。

Firstly, some basic properties of the limit shadowing are given; Secondly, we give the characterization of both lin-ear automorphisms and linear flows on R~ with the limit shadowing property; Thirdly, as applications we prove that the hyperbolic endomorphisms on T~ have the limit shadowing properties, Smale "horseshoes" have the same prop-...

首先，给出了极限跟踪性的一些基本性质；其次，得到了n维欧氏空间上线性自同构及线性流具有极限跟踪性的特征；最后，作为应用证明了双曲环面自同态以及Smale&马蹄&在其不变集上具有极限跟踪性。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。