关于弱交换PO-半群中的一个问题

ON A PROBLEM IN WEAKLY COMMUTATIVE PO-SEMIGROUPS

本文引入弱交换ｐｏ－半群的概念，研究这类半群到其Ａｒｃｈｉｍｅｄｅａｎ子半群的半格分解，得到了这类半群类似于具平凡序的弱交换半群的一个特征，由此在更一般的情形下回答了Ｋｅｈａｙｏｐｕｌｕ在［１］中提出的一个问题，并作为推论得到弱交换ｐｏｅ－半群和具平凡序的弱交换半群的已知结果．

In this paper we intruduce the concept of weakly commutative po-semigroups, we initiate the Study of the scmilattice decompositions of this type of semigroups into their archimedean subsemigroups and give a characterization of such semigroups analogous to that of weakly commutative semigroups without order. As a result. a problem raised by Kehayopulu in [1] is answered in more general case, and the known results on weakly commutahve poe-semigroups and weakly commutativc senigroups without order are obtained.