半遗传环上的群环  

GROUP RINGS OVER SEMIHEREDITARY RINGS

作　　者：陈焕艮[1] 冯良贵[1] 

机构地区：[1]南京大学数学系

出　　处：《南京大学学报（自然科学版）》1995年第3期357-361,共5页Journal of Nanjing University（Natural Science）

摘　　要：研究了半遗传环上群环上的投射棋的结构，证明了：（１）设Ｒ为下列环之一：（ａ）半遗传局部环；（ｂ）零维环，ｂ为有限生成的Ａｂｅｌ群，且满足下列条件之一：（ｃ）｜ＴｏｒＧ｜∈Ｕ（Ｒ）；（ｄ）ｃｈａｒＲ＝Ｐｓ（ｓ≥１），则Ｋ。ＲＧ为无挠群．（２）设Ｒ为半遗传环且ｃｈａｒＲ≠０，Ｑ为有限生成的Ａｂｅｌ群，则Ｋ。ＲＧ为挠群当且仅当Ｋ。Ｒ为挠群且如果Ｇ有素数Ｐ阶元，则ＰＵ（Ｒ）。We study the structure of the projective moduled over semihereditary rings.We have proved that if R is a semiliereditary ring and G is torsion--free then K。RG ∽K。R. As its application, we give the following results:(1)Let R be one of tile following rings ;(a)the semihereditary semilocal rings;(b)the zero--dimensional rings;G be a finitely generated abelian group, R and G satisfy one of the followingconditions;(c) | TorG | ∈ U (R) ;(d)charR=ps (s≥1)Then K。 RG is torsion--free.(2) Let R be a semihereditary ring with charR ≠ 0, G be a finitely generated abeliab group, then K。 RG is a torsion group if and only if K。 R is a torsion group and if G has an element of prime order P then P u(R)At last, we give the characteristic of semihereditary ring with torsion reduced group.That is,R is a semihereeditary ring with torsion reduced group if and only if there exists some s>o such that Ps is free for any finitely generated semi-reflexive R--module P.

关 键 词：约化群 群环 半遗传环 G环 

分 类 号：O153.3[理学—数学]