格序群的上下子群和Saturated子群的构造

Construction of the Above and Below Subgroups and Saturated Subgroups of l-groups

中文摘要:

      本文对[1]中关于极大上下对的公开问题给出否定的回答并构造了例子说明[2]中命题2.1证明过程中的错误;研究了saturated子群的构造,得到了任意ι-群的正交子集生成的saturated子群以及投射ι—群的任一子集生成的saturated子群的具体形式.

英文摘要:

      In this paper, an open question on maximal above and below pairs is answered nega-tively and an example is given to show the incorrectness of the proof for Proposition 2.1 in [2]. Furthermore, the construction of saturated subgroup is discussed. The forms of the saturated subgroup generated by a disjoint subset in an l-group and the saturated subgroup generated by any subset in a projectable l-group are determined.