阿贝尔群的完整子半群的若干结果

Some Results of Total Subsemi-groups of Abelian Groups

本文证明了无扭阿贝尔群Ｇ是唯一线性序的，当且仅当Ｇ的每一个完整子半群只含唯一的极小完整子半群．若群Ｇ的每一个完整子半群只含有限多个极小完整子半群，则Ｇ中所有完整子半群组成的集Ｔ（Ｇ）满足ＤＣＣ．

The main results obtained in the present paper are the following tWo assertions: (1)Atorsion-free abelian group is uniquely linear-ordered if and only if every total subsemi-group contains uniquely minimal total subsemi-group.(2)If every total subsemi-group of a commutative group contains only finitely many minimaltotal subsemi-groups,then the set T(G)which consists of all total subsemi-groups satisfies thecondition DCC.