ideal of a Lie algebra

例句：

1. 1. The ideal of a free and peaceful society is something that we all strive for.
   自由和平的社会的理想是我们所有人努力追求的目标。
2. 2. The scientist's ideal was to find a cure for cancer.
   这位科学家的理想是找到治疗癌症的方法。
3. 3. The company's mission is to provide quality products at affordable prices.
   该公司的使命是在提供物美价廉的产品。