模的半同态

Half Homomorphism of Modules

证明了模的半同态或同态或是反同态，即若Ｒ是环，Ｍ和Ｍ′是Ｒ双模，为Ｍ到Ｍ′的一个映射，且满足：ｘ，ｙ∈Ｍ，φ（ｘ＋ｙ）＝φ（ｘ）＋φ（ｙ）；ｘ∈Ｍ，ａ，ｂ∈Ｒ，φ（ａｘｂ）＝ａφ（ｘ）ｂ或φ（ａｘｂ）＝ｂφ（ｘ）ａ，则φ是模Ｍ的一个同态或反同态。

It is proved that a half homomorphism from R double module M onto R double module M ′ is a homomorphism or an anti homomorphism. Meanwhile, Hua’s proof of the corresponding theorem of a ring can be simplified with the method presented in this paper.