free associative ring

例句：

1. 1. The researchers found that the free associative ring was crucial to the success of their experiment.
   研究人员发现，自由关联环对于实验的成功至关重要。
2. 2. The free associative ring allowed for easy communication between different departments within the company.
   自由关联环使得公司内部不同部门之间的沟通变得简单。
3. 3. The free associative ring is a fundamental concept in the field of computer science.
   自由关联环是计算机科学领域的基本概念。