平坦模与内射模对偶性的一个注记

A Note on Duality of Flat Module and Injective Modules

我们从投射模和内射模的交换图定义中,可以发现它们是对偶命题,可随着研究的深入,发现它们的对偶性不是很好,例如所有的内射模都有内射包络,而所有的投射模不一定有投射覆盖.本文从维数角度给出了内射模和平坦模的一个等价刻画,从而再次说明了内射模和平坦模具有更好的对偶性.

We found that projective module and injective module are a good dual proposition from the definition of commutative diagram. But with further study, we find their duality are not fine. For example, all injective modules have injective envelope, but some projective modules have not projective cover. This article from viewpoint of dimension obtained an equal characterization of injective module and flat module with better duality.