自由可换格群的阿基米德性质

ARCHIMEDEAN PROPERTY OF A FREE ABELIAN LATTICE GROUP

S.J．Berun曾给出了在一个半序群上的自由可换格群是阿基米德的充要条件．但是他的证明中含有一个错误．我们将改进Bernau的结果，用简单的方法给出另一个充要条件．同时我们还给出了如何判别一个格群是阿基米德的充分条件．

S. J. Bernau gave a necessary and sufficient condition in which the free abelian lattice group on a ordered group is archimedean. But his proof contains an error. We will improve Bernau's result and give another necessary and sufficient condition using a simplemethod. We also give a sufficient condition in which an lattice group is archimedean.