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1·When a direct sum of lifting modules is lifting is studied here.

研究了提升模的任意直和在什么条件下仍是提升模。

2·An integral extension construction of domains was also derived by using the semi-direct sum of rings.

同时，还证明了半直和的剩余类环是整环的一个整扩张。

3·We introduce the notion of topological direct sum, and get a representative theorem of inductive limit by topological direct sum and quotient space.

然后引入拓扑直和的概念，利用它和商空间给出一个归纳极限表示定理。

4·According to algebraic property that a direct sum of Galois fields is isomorphic to a finite ring, the linear block code for multiplexing systems is proposed.

依据有限域直和与有限环同构的代数性质，对多路复用系统构造线性分组码。

5·The definition of similar quasi-direct sum of matrix is introduced. Andthe connection with group inverse is discussed. Some properties and applications are obtained.

首先引入矩阵的相似准直和的定义，讨论了它和群逆的关系，得到了一些性质和应用．。

6·In this paper, we have discussed root subspace decomposition of linear space, and for the linear space have decomposed direct sum of root subspace, a primary proof is given.

文章讨论了线性空间的根子空间分解，并对线性空间分解成根子空间的直和给出了较为初等的证明。

7·This paper presents that the sum of the value register of linear transformation and thenucleus is a full and necessary condition for direct sum, and from which five inductions are obtained.

给出了线性变换的值域与核的和是直和的充要条件，并由此得到五个推论。

8·The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given, and it was used in the proof of some equality about the rank of idempotent matrix.

给出了两两互素多项式下线性变换的核的直和分解，并应用于幂等矩阵（对合矩阵）的秩的等式证明中。

9·This month, for example, it added the option to make direct payments to its service, letting users donate a specified sum directly to a website.

例如，本月它增加了直接为其服务付款的功能，让用户直接为网站支付特定数额。

10·If a DataNode's load level is greater than the sum of its neighbors, then load-destination nodes (direct neighbors and other nodes) will be chosen at random.

如果DataNode的负载级别大于其邻近节点，将随机选择那么负载目标节点(直接相邻的节点及其他节点)。