群环上的幂自由模

Modules with Free Powers over Group Rings

中文关键词:  Artin环  K₀群  特征

英文关键词:Artin ring  K₀-group and characteric.

中文摘要:

      本文证明了：设Ｒ为ｃｈａｒＲ≠０，Ｇ为有限生成的Ａｂｅｌ群，则：Ｐ∈Ｆ＝（ＲＧ）当且仅当ｓ＞０，使得Ｐ^ｓ∈Ｆ＝（ＲＧ）．

英文摘要:

      In this paper, we obtain the following result: Let R be ring with char R≠0, G be a finitely generated abelian group. Then P is a finitely generated free RG-module if and only if there exists some s>0 such that P^ｓ is a finitely generated free RG-modules.