有常秩的投射模

Projective Modules of Constant Rank

本文定义更具一般性的模（未必是有限生成投射模）的常秩的概念，并证明了如果M有常秩n，∧^n M是有限生成的，则M是有限生成的,还证明了若M是有常秩n的投射模，则M一定是有限生成的。

In this note we define the notion of the constant rank of modules （not necessarily finitely generated projective modules） and prove that if M is of constant rank n and ∧^n M is finitely generated, then M is finitely generated, and that if M is a projective module of constant rank n, then M is finitely generated.