格序群中的序群与有效性
Ordering groups and validity in lattice-ordered groups
摘要：
给出了一个群的子集的一个特征，该群的子集延伸到群上的右阶正锥，并用于将格序群（l-群）中方程的有效性与自由群的子集延伸到右阶正锥联系起来.这种对应关系被用来获得新的证明的可判定性字问题的自由l-群和产生的各种l-群的l-自同构群的实数行。群的子集延伸到群上的阶的正锥的特征也被用来建立各种可表示的l-群（等价地，序群的类）和相对自由群的子集延伸到阶的正锥的方程的有效性之间的对应。
英文摘要：
A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered groups (l-groups) to subsets of free groups that extend to positive cones of right orders. This correspondence is used to obtain new proofs of the decidability of the word problem for free l-groups and generation of the variety of l-groups by the l-group of automorphisms of the real number line. A characterization of the subsets of a group that extend to the positive cone of an order on the group is also used to establish a correspondence between the validity of equations in varieties of representable l-groups (equivalently, classes of ordered groups) and subsets of relatively free groups that extend to positive cones of orders.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
