交换格序群等距的若干性质

SOME PROPERTIES OF ISOMETRIES ON ABELIAN LATTICE-ORDERED GROUPS

设Ｔ是交换格序群Ｇ的稳定等距。在这篇文章中，利用交换格序群可表为全序群的亚直积这特点．证得对×∈Ｇ．有Ｔ（ｘ）＝（Ｔ（ｘ）１．Ｔ（ｘ）２…７（ｘ）ｉ…）＝（ε１ｘ１．ε２ｘ２…εｉｘｉ…）．其中Ｔ（ｘ）ｉ＝εｉｘｉ＝±ｘｉ．进而得到交换格序群Ｇ等距的若干性质。

Let T be a stable isometry of the Abelian Lattie -Ordered group G. In this paper itshows you that T (x)=(T (x)i…T (x )i… )=(ε1x1, e2x2, …ε1x1…)for each x ∈G (where T (x )i = + ε1,xi = ±xi) by every such group can be written as a subdirect product of totally ordered groups Ga, a ∈ A. Further propertics of isometries on abelian Lattice - ordered groups can be obtained by the theorem.