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1.The pseudo free ideal ring is a theoretical construct that has been proposed to explain the behavior of certain systems.
伪自由理想环是理论上的一个构造，被提出来解释某些系统的行为的。
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2. In this study, we explore the pseudo free ideal ring in the context of quantum computing.
在这个研究中，我们探索了伪自由理想环在量子计算的背景下。
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3.The pseudo free ideal ring is a mathematical concept that has been used to model complex systems.
伪自由理想环是一个数学概念，被用来模拟复杂的系统。