Abstract: In the paper, the relevant properties of subcoframe and co-frame homomorphism and connections among them with application are studied. Firstly the basic properties of subcoframe and co-frame homomorphism are discussed. Secondly, the properties of co-frame homomorphism related subcoframe are investigated. Thirdly, the properties related two parallel having same domain and same codomain are investigated by co-frame and embedding mapping. At last, the properties related the family of co-frame injective homomorphism having same codomain and pointing to single direction are investigated. The work of the paper is of worth as reference in studying of co-frame homomorphism.

Key words: lattice theory, co-frame, subcoframe, homomorphism, parallel homomorphim, injective homomorphism

摘要： 针对子余Frame和余Frame同态的相关性质以及两者之间的联系和应用进行了研究。首先对子余Frame及余Frame同态的相关性质进行了讨论；其次讨论了子余Frame和余Frame同态相结合的相关性质；第三，子余Frame和嵌入映射讨论了具有相同论域和余论域的两个平行余Frame同态的相关性质；最后，对具有相同论域的单向余Frame单同态族的性质进行了研究。该文的结果在关于余Frame同态的研究工作中具有参考价值。

关键词: 格论, 余Frame, 子余Frame, 同态, 平行同态, 单同态族