论文标题
Frobenius Foundors和Gorenstein投射重剂
Frobenius functors and Gorenstein projective precovers
论文作者
论文摘要
我们在Frobenius Foundors连接的Gorenstein投射重植物之间建立了关系。这是一个开放问题的动机，即如何找到模块具有Gorenstein投射重植物的一般戒指。结果表明，如果$ f：\ c \ rightarrow \ d $是具有足够投影对象的阿贝尔类别之间可分离的frobenius functor，则$ \ c $中的每个对象都有gorenstein jupparive repover，前提是$ \ d $中的每个对象都有Gorenstein Projective projective repover。该结果应用于可分离的Frobenius扩展和出色的扩展。
We establish relations between Gorenstein projective precovers linked by Frobenius functors. This is motivated by an open problem that how to find general classes of rings for which modules have Gorenstein projective precovers. It is shown that if $F:\C\rightarrow\D$ is a separable Frobenius functor between abelian categories with enough projective objects, then every object in $\C$ has a Gorenstein projective precover provided that every object in $\D$ has a Gorenstein projective precover. This result is applied to separable Frobenius extensions and excellent extensions.
