$K{\mathbb{Z}}^{\left(n\right)}$上分次扩张的子环

Subrings of Graded Extensions in $K{\mathbb{Z}}^{\left(n\right)}$

摘要: 斜群环是一类非常重要的环，其上的分次扩张是一类非常重要的环扩张。本文在$K{\mathbb{Z}}^{\left(n\right)}$ 上分次扩张的基础下，研究了$K{\mathbb{Z}}^{\left(n\right)}$ 上分次扩张的子环，利用锥的理论证明了$K{\mathbb{Z}}^{\left(n\right)}$ 上分次扩张的子环与之相对应的锥的集合有一个一一对应关系。

Abstract: Skew group rings are a very important class of rings, and the graded extensions over them are a very important class of ring extensions. In this paper, based on the graded extensions over $K{\mathbb{Z}}^{\left(n\right)}$ , we study the subrings of the graded extensions over $K{\mathbb{Z}}^{\left(n\right)}$ . By using the theory of cones, it is proved that there is a one-to-one correspondence between the set of subrings of the graded extensions over $K{\mathbb{Z}}^{\left(n\right)}$ and the set of corresponding cones.