K[G,σ]上分次扩张的子环与超环  

The Subrings and the Over-rings of Graded Extensions in K[G,σ]

作　　者：刘正堂 罗鑫鑫 陆修灿 Liu Zhengtang;Luo Xinxin;Lu Xiucan(College of Mathematics and Statistics Guangxi Normal University,GuangxiGuilin,541004)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《科技风》2021年第24期75-76,82,共3页

摘　　要：设V是除环K的全赋值环,G是一个有纯锥P的加群,σ:G→Aut(K)是一个群同态。假设G在K上的斜群环K[G,σ]有左商除环Q(K[G,σ])。令A=■_(u∈G)A_(u)X^(u)是V在K[G,σ]上的一个分次扩张。本文对A的子环和超环进行了研究,证明了A的子环和超环构成的集合与相应群某些锥的集合之间有一个一一对应关系。Let V be a total valuation ring of a skew field K,G be an additive group with a pure cone,σbe a group homomorphism from G to Aut(K).Suppose that the skew group ring K[G,σ] of G on K has a left quotient skew field Q(K[G,σ]).Let A=■_(u∈G)A_(u)X^(u) be a graded extension of V in K[G,σ].In this paper,the subrings and over-rings of A are studied,and it is shown that there is a one-to-one correspondence between the sets of subrings and over-rings of A and the sets of certain cones of the corresponding groups.

关 键 词：全赋值环 分次扩张 子环 超环 

分 类 号：O153.3[理学—数学]