名词短语
中文翻译：有限生成的自由模块
同义词：
['finitely generated free module', 'finitely generated free module', 'finitely generated free module例句：1. The finitely generated free module is a crucial component of the computer architecture.（有限生成的自由模块是计算机体系结构的关键组成部分。）']
例句：
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1. The finitely generated free module is a crucial component of the computer architecture.
有限生成的自由模块是计算机体系结构的关键组成部分。
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2. In the field of computer science, finitely generated free modules are used to study the properties of linear transformations.
在计算机科学领域，有限生成的自由模块被用来研究线性变换的性质。
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3. The finitely generated free module theory has been applied to the design of digital circuits and the optimization of hardware systems.
有限生成的自由模块理论已经被应用到数字电路的设计和硬件系统的优化中。