中文摘要：

通过引入 Jordan 多重同态、多重同态和布尔同态的概念，利用布尔同态给出有1结合环上 Jordan 多重同态的结构，并讨论一些特殊环上布尔同态的一般形式。结果表明，有1结合环上 Jordan 多重同态即为多重同态。

英文摘要：

We introduced the notions of Jordan multi-homomorphisms,multi-homomorphisms and Boolean homomorphism.Using Boolean homomorphisms,we described the structures of Jordan multi-homomorphisms on associative rings with identity,and then showed that a Jordan multi-homomorphism is a multi-homomorphism on associative rings with identity,and finally,gave general forms of Boolean homomorphisms on some special rings.