中文摘要：

当它的 unary 操作是趋于增加的并且是复杂物时，我们构造免费 Hom-semigroups。我们建设的方法由括的词。作为后果，我们获得一个集合为 unary 操作在一样的条件下面产生的免费 Hom 联合的代数学。

英文摘要：

We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.