环的约化群与群环上的投射模  

Reduced Groups of Rings and Projective Modules over Group Rings

作　　者：陈焕艮[1] 

机构地区：[1]湖南师范大学数学系

出　　处：《数学学报（中文版）》1995年第6期759-765,共7页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：本文系统地研究群环的约化群，利用约化群刻划了群环上模的结构。主要结果：（１）Ｒ为交换半遗传环且Ｋ＿０Ｒ为挠群ｉｆｆ对任何有限生成半自反Ｒ－模Ｐ，ｓ＞０，使得．（２）设Ｒ为半局部Ｄｅｄｅｋｉｎｄ环，Ｇ为有限生成Ａｂｅｌ群，则Ｋ＿０ＲＧ为挠群ｉｆｆ如果Ｇ有素数ｐ阶元，则（３）如果Ｋ＿０ＲＧ为挠群，［Ｇ∶Ｈ］＜∞，则对任何，有．这里Ｒ为整环，Ｌ为其分式域。In this paper,we consider reduced groups of group rings.As applications,we obtainthe following results:(1)R is a commutative semihereditary ring with torsion reduced group if and only if there exists some s > 0 such that for any finitely generated semireflexiveR-module P.(2)Let R a semilocal Dedekind domain,G be a finitely generated abellan group.Then K_0RG is a torsion group if and only if whenever G has some element of primeorder p.(3)Suppose K_0RG is a torsion group. If L is the fractional field of integral domain Rand [G∶H]<∞,then for any .

关 键 词：约化群 半自反模 环 群环 投射模 

分 类 号：O153.3[理学—数学]