交换环上有限生成自由模的一个性质

One Property of Finite Generated Free Modules over a Commutative Ring

用交换代数及同调代数的方法证明了交换环上有限生成自由模的一个性质，并举例说明有限维向量空间中向量组的秩这一概念，不便于推广到交换环上有限生成自由模的情形．

In this paper,it proves one property of finite generated free modules over a commutative ring,which is generalized from funite dimensional vector space- Accoring to the discussion,it points out that the rank of a vector set can not be spread in finite generated free modules over a commutative ring.