关于赋值环的单元群

On Groups of Units of a Valuation Ring

中文摘要:

      

英文摘要:

      Let K be a field, K^* be the multiplicative group of nonzero elements of K and S be a subgroup of K^*. In this paper we show that S is a group of units of a valuation ring of K if and only if S satisfies the following conditions:1.a∈S implies -a∈S;2. for any a∈K^*\S either a S?S or a^-1 S?S. Additional properties cf such groups are included.