อ้างอิง:
ข้อความเดิมเขียนโดยคุณ mercedesbenz
Proof: We want to show that
$\sum_{i\in I}C_i=<\{v_{i}|i\in I\}>$.
Consider $<\{v_{i}|i\in I\}>=\{n_{i_1}v_{i_1}+n_{i_2}v_{i_2}+\cdots+
n_{i_k}v_{i_k}:i\in I,n_{i_j}\in \mathbb{Z},1\leq j \leq k\}$ (It's wrong or right)
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ถูกครับ
อ้างอิง:
Clearly $\{v_{i}|i\in I\}>\subset \sum_{i\in I}C_i $.
then I want to show $\sum_{i\in I}C_i \subset <\{v_{i}|i\in I\}>$.
Please help show next step.....
thank you for any help.
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Let $x\in\sum_{i\in I}C_i$. Then $x=\sum_{k=1}^nb_{i_k}$ for some $b_{i_k}\in C_{i_k}$
Since $C_{i_k}$ is generated by $a_{i_k}$, $b_{i_k}=...$