K ℤ ( n ) 上分次扩张的子环  

Subrings of Graded Extensions in K ℤ ( n )

作　　者：陆修灿 

机构地区：[1]桂林信息科技学院基础教研部,广西 桂林

出　　处：《理论数学》2025年第2期93-97,共5页Pure Mathematics

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Kℤ(n)上分次扩张的基础下,研究了Kℤ(n)上分次扩张的子环,利用锥的理论证明了Kℤ(n)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。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 Kℤ(n), we study the subrings of the graded extensions over Kℤ(n). 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 Kℤ(n)and the set of corresponding cones.

关 键 词：斜群环 分次扩张 子环 锥 

分 类 号：O15[理学—数学]