semigroup homomorphism

例句：

1. 1. In thestudy of linear algebra, the concept of a semigroup homomorphism is crucial for understanding the behavior of functions between two groups.
   在线性代数研究中，半群同态的概念对于理解两个群之间的函数行为至关重要。
2. 2. The development of the theory of semigroup homomorphism has greatly advanced our understanding of group actions and theirapplications in various fields.
   半群同态理论的发展极大地推动了我们对群作用及其在各个领域应用的理解。
3. 3. The research on semigroup homomorphism has led to significant advances in the field of computer science, as it provides a powerful tool for studying the behavior of algorithms within a group structure.
   关于半群同态的研究已经为计算机科学领域带来了显著的进步，因为它为研究算法在群结构内的行为提供了一种强大的工具。