non-commutative local ring

例句：

1. 1. The non-commutative property of the material makes it useful in certain applications.
   这种材料的非交换性质使其在某些应用中非常有用。
2. 2.In physics, a non-commutative ring is a ring that is not commutative with respect to its multiplication operation.
   在物理学中，一个非交换环是指在其乘法运算中不是可交换的环。
3. 3. The non-commutative nature of the system means that it cannot be easily modeled using traditionalmathematical methods.
   该系统的非交换性质意味着它不能用传统的数学方法轻易地建模。