交换半群上的次范整线性空间

Sub-normed Z-linear Spaces on Commutative Semi-group

为了刻画和研究平移空间的线性结构,给出了平移半群的概念,在平移半群为满足相消律的交换半群的平移空间上,引入了整数系数的线性结构;再加之,在平移空间上可利用距离在一定条件下构造出线性结构,引入了次范整线性空间的定义;并且证明了平移空间是次范整线性空间的充要条件是它的平移半群是满足相消律的交换半群.

In order to describe the linear structure on translation spaces,this paper provides the concept of the translation semi-group;The linear structures of integer coefficient is introduced by the translation spaces on the translation semi-group that is satisfied with cancellation law.Furthermore, it is proved that linear structures can be constructed by means of metrics on translation spaces under certain conditions.The concept of sub-normed Z-linear spaces is introduced and it is clarified that a translation space is a sub-normed Z-space if and only if its translation semi-group is the commutative semi-group that is satisfied with cancellation law.