偏序带的偏序扩张

On Extensions of Partial Orders of Partially Ordered Bands

给出将偏序幺半格和偏序带S·≤上的偏序≤扩张为全序幺半格和带S·≤的充要条件。作为应用,得到文献1结论:设S·是幺带,存在S上的平凡序的全序扩张≤使得S·≤是全序幺带当且仅当S的每个D类至多有两个元素。

In this paper, the sufficient and necessary conditions for extending partial orders of partially ordered semi-lattices and partially ordered bands to linearly orderes are given. By way of application, the result is obtained that there exists a total order on a band with identity so that it is a totally ordered band only if every D class has at most 2 elements .