关于交换格序群保持内在度量映射的一个定理

A THEOREM OF INTRINSIC METRICS PRESERVING MAPS ON ABELIAN LATTICE￣ORDERED GROUPS

本文通过讨论，证得：若Ｇ１．Ｇ２是交换格序群，ｆ是Ｇ１到Ｇ２的保持内在度量映射，则ｆ是Ｇ１到Ｇ２的群同态当且仅当ｆ（－ｘ）＝ｆ（ｘ）．该定理部分解答了Ｅｎｄｒｅｐａｐ在文章《交换格序群保持内在度量映射》中提出的一个问题．

This theorem shows you that Let G 1 and G2 be abelian lattice-ordered groups, jis a intrinsic metrics preserving map from G1 to G2, then j is a homomorphism if andonly if f (-x)=-f (x). The theorem gives the partial answer to a question proposedin the paper hintrinsic metrics preserving maps on abelian lattice-ordered groups' written by Engdre pap.